during a visit to the Catskills. Cooper set his story on the frontier, in a liminal, contested space at the edge of "civilization," one that had to be navigated with the help of Native American guides. The book thus explores the beauty to be found in an American wilderness frontier, such as in this quote from chapter 3:

The rays of the sun were beginning to grow less fierce, and the intense heat of the day was lessened, as the cooler vapors of the springs and fountains rose above their leafy beds, and rested in the atmosphere. Still that breathing silence, which marks the drowsy sultriness of an American landscape in July, pervaded the secluded spot, interrupted only by the low voices of the men, the occasional and lazy tap of a woodpecker, the discordant cry of some gaudy jay, or a swelling on the ear, from the dull roar of a distant waterfall.

Another characteristic of American Romanticism is a favoring of the young, vigorous American democracy as a better system than the moribund old ways of Europe. We find that sentiment expressed in chapter one:

But, emulating the patience and self-denial of the practiced native warriors, they learned to overcome every difficulty; and it would seem that, in time, there was no recess of the woods so dark, nor any secret place so lovely, that it might claim exemption from the inroads of those who had pledged their blood to satiate their vengeance, or to uphold the cold and selfish policy of the distant monarchs of Europe.

Finally, American Romantics tended to romanticize and "other" Native Americans, and while they are shown massacring, they are also depicted as closer to nature than white people (Natty, for example, cannot believe an Indian would ever get lost in the woods), and nostalgically mourned for their passing out of power. At the end of the book we learn:

The pale-faces are masters of the earth, and the time of the red-men has not yet come again.

This plays on our emotions, another hallmark of Romanticism, both American and European.

The three characteristics of Romanticism in the novel are nostalgia, individualism, and connection to nature. One of the hallmarks of Romanticism in literature is a yearning for the past and for what is authentic. The Last of the Mohicans is nostalgic about the past and about the time when Mohicans were plentiful. As the last Mohican alive, Chingachgook is a Romantic figure who embodies the idea of the "noble savage." He is at home with nature and the natural world and represents the romantic ideal of someone who was a remnant of the past.

Natty Bumppo, known as Hawkeye, is a Romantic character because he is a rugged individualist who lives according to his own sense of what is right and how he feels. He befriends Native American people, showing his connection to a people who are pure and closely connected to nature. He lives in harmony in the natural world, another hallmark of Romanticism. He is not subject to the laws of civilization but lives according to his own sense of morality, making him a truly Romantic figure. 

There are many examples of American Romanticism (a version of the English Romantic movement that occurred some years earlier) in James Fenimore Cooper's novel The Last of the Mohicans.

"Shuns civilization and seeks nature" is seen with the character of Hawkeye. He has a close alliance with certain Native American tribes, however, he is a white man who has chosen to live in the wilderness rather than amid "civilized white men." And while it is important that he maintain his identity as a white man, he finds his strongest friendship with Chingachgook, the "last of the Mohicans."

Hawkeye also embodies the characteristic of "fights for individual's freedom and worth." He fights to save Alice and Cora from Magua. He also helps others of their group escape not only from the Indians (i.e. Major Heyward), but also from the French (i.e. Colonel Munro).

"Finds beauty and truth in supernatural or imaginative realms" also applies to Hawkeye. Whereas Gamut is a religious man, he is ineffective in the wilderness. Hawkeye is not religious in terms of organized religion: he may actually be seen as a pagan in light of this. However, ironically, it is Hawkeye's ability to find beauty and truth in nature that makes him a much more spiritual person than David Gamut. Hawkeye is also a superstitious man, which would bring to light the "imaginative realms" in his system of belief.

The Last of the Mohicans is part of a very popular series of novels written by James Fenimore Cooper. YThese novels have several features characteristic of American Romanticism.

The most obvious characteristic is the treatment of Native Americans. They are portrayed either as barbaric or noble savages, with both portraits being equally stereotyped. The Noble Savage is a standard Romantic trope, in which distance of a culture from western civilization is identified with a form of instinctive nobility and closeness to nature.

The extended description of wilderness and intense emotion reaction to untamed nature are typical or romanticism.

Finally, the heroines, who in spite of all probability, remain beautiful and virginal through many dire perils is another feature typical of romanticism – and romance literature.

According to the criteria you helpfully provided, at least three characters in James Fenimore Cooper’s novel The Last of the Mohicans can be classified as “American Romantic heroes.”  Those three characters are the following:

• Natty Bumpo (“Hawkeye”): Hawkeye is very familiar with nature in general and with the forest in particular. He knows how to survive in the woods and is also skilled in handling a canoe on the river. He and his two Native American friends, Chingachgook and the latter’s son, Uncas, actually escape from danger at one point by floating down a river, thus demonstrating their resourcefulness and bravery. Hawkeye and his friends are also heroic in the way they attack the Hurons who have captured some white soldiers and two white women. Hawkeye is skilled in tracking animals and people, as when he traces the location of the white women after finding a veil belonging to one woman hanging from a tree. Hawkeye shows heroic bravery when he wears a disguise and manages to sneak into an enemy camp. As the novel concludes, Hawkeye uses his rifle to slay Magua, a Huron who is the major antagonist of most of the heroic characters in the book.

• Chingachgook: a brave Mohican chief, Chingachgook is a loyal friend to Hawkeye and courageously helps Hawkeye whenever the latter needs assistance. Chingachgook is a determined fighter and, as is customary, scalps some of the people he kills. When his own son, Uncas, is killed at the end of the novel, Chingachgook finds comfort in Hawkeye’s friendship:

Chinachgook grasped the hand that, in the warmth of feeling, the scout had stretched across the fresh earth, and in an attitude of friendship these two study and intrepid woodsmen bowed their heads together, while scalding tears fell to their feet, watering the grave of Uncas like drops of falling rain.

• Uncas: Uncas, a Mohican brave, is young, good-looking, courageous, and romantically attracted to one of the one of the main female characters, Cora. He uses his own familiarity with nature to help find her after she is kidnapped. He is a good and loyal friend to Hawkeye and a worthy son of his father, Chingachgook. Uncas assists his father and Hawkeye in all their heroic schemes, and when he is captured by their enemies he manages to use a disguise to help free himself from captivity. As the novel concludes, Uncas dies in hand-to-hand combat while trying to rescue Cora.

Hawkeye, Chingachgook, and Uncas thus display many of the traits you listed as characteristic of an American Romantic hero: Uncas is youthful; all three men have a strong sense of honor based on principle; all three display knowledge that comes from intuitive learning, experience, and common sense rather than from formal schooling; all three love nature over life in towns; all three are brave; Uncas is handsome; and Hawkeye in particular seems to possess almost superhuman abilities, as when he manages to shoot, from a long distance, a Huron who was just about to stab a friend.

One of the most distinct qualities of Romanticism that Cooper highlights is the idea of understanding the connection between the past, the present, and the future.  The very idea of "the last" of a group or a tribe is a Romantic ideal. It seeks to link the individual back to generations that have already come and gone.  Romanticism sought to link the present to the past, almost suggesting that there is an indelible connection between the two.  The modern individual is not alone in their consciousness, something that is illuminated in the text: "When Uncas follows in my footsteps, there will no longer be any of the blood of the sagamores, for my boy is the last of the Mohicans." The idea of heritage and linkage between the past and the present is a Romantic quality that is at the forefront of Cooper's work.

The death of the tribe and the corruption that modern society possesses is another Romantic quality that is illuminated in the work.  White interaction with the Mohicans has been destructive and has hastened their elimination.  "Conventional" and "conformist" society is seen as bad, something to be repelled in the name of that which exists outside of it.  This is a Romantic trait that Cooper holds to in the narrative's development.  The narrative is told with this reality in mind:  "The pale faces are masters of the earth, and the time of the redmen has not come again. My day has been too long ... I have lived to see the last warrior of the wise race of the Mohicans."  This is Romantic in scope because it seeks to glorify that which is passing.  Cooper demonstrates a Romantic nostalgia for what has succumbed to modern society and modernization.  This is a Romantic quality that drives the text, one that becomes a "tribute to the vanishing cultures of the Native Americans."

Generally speaking, authors accomplish characterization directly or indirectly, depending on the point of view of narration. Direct characterization is achieved by description of the way the character looks and acts. Indirect characterization happens when the narrator presents how the character thinks, acts, speaks, or interacts with others.

In The Last of the Mohicans, James Fenimore Cooper relies on both direct and indirect characterization. This is notable in chapter three with the narrator's description of Nathaniel, also known as Hawkeye or Long Rifle. He is described as "muscular" with "an expression of sturdy honesty." Despite being a white man, he speaks in the language of the natives. Based on how he describes himself and what he has to say about life on the frontier, Nathaniel is comfortable walking in both the world of whites and natives and knows that there is blame on both sides for the hostilities between the two. His clothing and accouterments draw from both white and native culture, and Cooper wants readers to see him as a hybrid of both cultures. Nathaniel's indirect characterization is seen in his state of mind when he argues with Chingachgook and is described as "a little nettled." Later in the same scene, Hawkeye is described by the narrator as "touched at the calm suffering" of Chingachgook as he relates the circumstances that will make his son Uncas the last of the Mohicans.