Why is Miyax alone and lost in Julie of the Wolves?

In short, Miyax is "alone and lost" because she has run away from her mentally ill husband, Daniel, in a desperate attempt to travel to her pen pal, Amy, in San Francisco.  Unfortunately, Miyax ends up in the Alaskan tundra during the one time of year (the Arctic summer) when it is almost impossible to determine both direction and location.

Miyax is coerced into marrying Daniel in order to escape from her Aunt Martha.  The marriage between Miyax and Daniel is an arranged marriage.  The moment Julie sees Daniel, she notices there "is something wrong with him."  It is not long before Daniel attempts to rape Miyax.  This is the event that causes Miyax to flee onto the Alaskan tundra.

One would think that an Eskimo as trained as Miyax would not be lost on the tundra, but at the time Miyax runs away, the north star (the ultimate guide for an Eskimo) is not visible.  The migration of the arctic terns aren't visible either (in that they have not started their migration).  Further, in the northern Alaskan summer, the sun never sets.  It simply circles the horizon.  Therefore, there is no way for Miyax to tell east from west.  

How does Miyax get lost in the Alaskan tundra at the start of Julie of the Wolves?

As we learn right at the start of Julie of the Wolves Miyax is lost. Not only that, but she's hungry and has been without food for "many sleeps" on the North Slope of Alaska.

Miyax never believed for one moment that she could ever get lost. As she tells the black wolf Amaroq, at home on Nunivak Island, the place where she was born, it was widely believed that plants and birds pointed the way for wanderers. She thought that this applied everywhere, not just her home island.

However, she's discovered to her cost that this isn't the case at all, and she finds herself without a natural compass to guide her. Because of this, two days previously, she came to the sudden realization that what she thought was the tundra was actually an ocean of grass on which she'd been circling around and around.

The fear that this realization caused has returned as Miyax closes her eyes. As she opens them, she is excited to see Amaroq looking right at her. But this is the only reason she has at this precise moment to be excited, as she is still hopelessly lost, far from her destination, and without anything to eat.

What is Miyax's desperate predicament in Julie of the Wolves?

Miyax's most life threatening predicament is survival.  She decided to run away from home and head toward San Francisco to meet her pen pal.  Unfortunately Miyax became hopelessly lost.  She is way out in the middle of the tundra with winter approaching.  She has minimal food supplies and does not have the proper food and shelter stuff to endure the coming winter weather.  

Miyax's other predicament is a cultural one.  I wouldn't call it desperate, because it's not life threatening in terms of stopping her heart from beating.  But it is life threatening in the sense that Miyax feels that she can't "live" her life the way that she wants to.  It's a bit of a twist for the reader to watch Miyax run away from a traditional Eskimo marriage.  She doesn't believe in such things.  A reader would think that she is making the push toward being more modern.  But after spending the winter on the tundra with the wolves and having to use the traditional Eskimo ways to survive, she has a disdain for modernization. She is appalled that her father now hunts with modern tools, so she runs away again to be more traditional.  

In Julie of the Wolves, why was Miyax afraid?

This question could be referring to several different parts of the book, but I think that it is likely asking about the opening events in part one of the book.  

Miyax is afraid because she is lost on the tundra of the North Slope of Alaska.  Miyax is afraid of her entire situation, because she is also without food.  

Miyax knows that her situation is fairly dire.  She needs food, and she needs it soon.  Her best option is to befriend a small wolf pack and convince them to share some of their food.  She's lost in the Alaskan wilderness with no food and is attempting to befriend wild wolves. . . yes, she's scared for a good reason.  

What's amazing about Miyax is that she isn't too afraid of the wolves themselves.  She is afraid that the wolves won't accept her and help her. That's her main concern, because it means death by starvation.  

Her hands trembled and her heartbeat quickened, for she was frightened, not so much of the wolves, who were shy and many harpoon-shots away, but because of her desperate predicament. Miyax was lost. She had been lost without food for many sleeps on the North Slope of Alaska.

How does Miyax overcome fear in Julie of the Wolves?

The answer to this question is quite simple: Julie/Miyax overcomes fear by concentrating on her survival. Allowing fear to overcome her means death to Julie. She must keep her wits about her because the Arctic winter is coming. Julie originally planned to escape to San Francisco in order to find her pen pal, Amy. Now that she has lost her way, she reverts to the old Eskimo ways that she knows so well (from living at the seal camp with her father). In order to take away her fear, Julie continually remembers her father's advice. Kapugen's advice is especially useful when she comes upon the wolf pack:

Wolves are brotherly. ... They love each other, and if you learn to speak to them, they will love you too.

More generally, we can see Julie overcome fear many times in the book. Julie builds a sod hut as soon as she realizes she is lost. Julie is very patient as she learns the wolves' mannerisms. Julie must have confidence in herself in order to become part of the pack. Once Julie realizes that lying belly-up is the ultimate submission (and what the pups always do to Amaroq), Julie uses this technique to submit to Amaroq. This bravery on Julie's part is what makes her part of the pack.

As you can see, in all of the instances above, Julie overcomes her fear by reverting to the "old ways" of the Eskimo and not allowing her mind to wander back to the dangerous feeling of fear.

What was Miyax afraid of in "Julie of the Wolves" and why?

This question is a bit tricky because I am unsure to which part of the book you are referring. I am going to venture a guess, however, that you are asking about Julie/Miyax when she plans to leave her arranged marriage. In that case, she fears a few things: that she will be sent back to her Aunt Martha, that she will continue to be raped, and/or that she will lose her way on the tundra. (Unfortunately, the third thing actually happens.)

First, Julie is afraid she will be sent back to her Aunt Martha. Julie is forced to live with her stern aunt in order to go to school. This separates Julie from her father and the seal camp where she is able to live in harmony with nature. The only way she can escape from Aunt Martha is by agreeing to the arranged marriage to Daniel.

Next, Julie is afraid of Daniel continually trying to rape her. Being a mentally ill young man, Daniel is not always in control of his own actions. He has tried once to rape Julie. There is no doubt he will try again.

Finally, Julie realizes the reality of being a lone person attempting to traverse the Alaskan tundra. She desires to make her way to San Francisco, but knows she has a slim chance of finding her way. Julie, then, fears death in this instance: death in the Alaskan wilderness.

In conclusion, the third fear partially comes true. Luckily, Julie comes upon the wolves, who accept her into their pack. Further, Julie eventually finds her father once again.

In Julie of the Wolves, what is Miyax's desperate predicament and how does it arise?

As the story begins, Miyax—or Julie, her American name—is all alone in the harsh wilderness of the North Slope of Alaska. She's in a whole lot of trouble, or in a “desperate predicament,” as the author puts it. Not only is she all alone in the middle of a brutal, unforgiving environment, she's also lost and hasn't eaten for days. Cold, hungry, and isolated, Miyax is in a very serious situation indeed.

So how on earth did she get into this mess? Well, it all started when Miyax ran away from an abusive arranged marriage. Miyax blames her husband, Daniel, a man described as “terrifying,” for the parlous situation in which she now finds herself. It was because of his abuse, what appears to have been an attempted rape, that Miyax decided to leave him and seek sanctuary with her pen pal Amy, who lives in San Francisco.

Miyax had intended to walk to Point Hope, where she would board a ship called the North Star, where she hoped to work her passage as a dishwasher or a laundress. Yet Miyax has found herself hopelessly lost in the wilderness, far from civilization, with no food and with only a pack of wolves for company.