Does Jake Barnes from The Sun Also Rises represent Hemingway's life?

One addition to the excellent answer above is that Hemingway had an extremely difficult time committing to a woman.  He was married several times and reportedly had numerous affairs. Readers can see that same struggle in Jake Barnes.  Jake seems to want to show love or affection to Brett but is unable to do so. This characteristic is typical of Hemingway's Lost Generation.  They roamed around Europe looking for adventure but were seemingly afraid of committing to anything, anybody, or any country. Just as Jake is on a quest for endless adventure, Hemingway spent most of his life traveling the world literally and figuratively hunting for the his next "game."

Yes, according to Enotes Hemingway bibliography:

In 1925 he began work on The Sun Also Rises which reflected his life in Paris among the “Lost Generation.”

In fact, Hemingway was inspired to write the novel on his 3rd visit to the San Fermin fiesta in Pamplona in the 1920s.

In terms of comparisons, both Hemingway and Jake Barnes are expatriate journalists, first in Paris and then Spain.  Both suffered war wounds from the Great War (WWI), although Jake never mentions how he received the wound (Hemingway, in fact, was not a soldier but an ambulance driver).  There, both Jake and Papa met other expatriates, namely Harole Leob (Cohn) and Lady Duff Twysden (Brett).  It was Jake's (Hemingway's) affection for Tysden (Brett) and jealousy of Leob (Cohn) that drives the narrator.

How does Hemingway depict Jake Barnes as the "hero" in The Sun Also Rises?

Two primary literary techniques Hemingway uses to establish Jake as the "hero," or central male character, are narratorial point of view and character relationships. First of all, Jake is the narrator of the story. While this does not in and of itself establish the narrator as the hero--there can be a narrator who is the focalizer who turns the focus on another character as the hero/heroine--Jake's relationship to and interactions with other characters confirms his role as hero.

The narrative is told by a subjective first-person narrator, Jake. Though this narrator is telling the story subjectively, he maintains some distance, which makes him a more reliable, less emotionally involved observer of other characters. Jake's position as focalizer of events and reactions, plus commentator on characters and events,

I rather liked him and evidently she led him quite a life.

establish him as the central character and protagonist, or hero, of the story.

This is confirmed because all the characters have some sort of relationship ties back to him. For instance, even Frances, who is Robert Cohn's girlfriend, is connected to Jake in that she reacts to his activities and remarks: this serves to take the focus from the subplot and re-establish the focus on Jake's experience. An example of this is in the early pages--in which Hemingway establishes the structure of the story--when Frances glares mercilessly and grows harder in her facial expression as Jake talks about a woman he knows in Alsace who can show him and Robert around on their projected--but vetoed--walking tour around Alsace.

I suggested we fly ... somewhere of other in Alsace. "I know a girl in Strasbourg who can show us the town," I said.
Somebody kicked me under the table. ... "she's a swell girl."
I was kicked again ... and, looking, saw Frances, Robert's lady, her chin lifting and her face hardening.
...I said, ... "We could go up to Burges, or to Ardennes."
Cohn looked relieved. I was not kicked again.

In this excerpted passage, the point of the characters being connected to Jake despite their own subplot is illustrated. Frances significantly reacts to Jake's suggestion and Cohn similarly significantly reacts by repeatedly kicking Jake under the table. This example shows their relationship to Jake, even though at the moment he has nothing to do with Frances directly. These are two techniques Hemingway uses to establish Jake as the protagonist, or hero, of the story.