As a strange god once said, writing is hard. It feels like there are near limitless aspects to consider during the writing process. With any luck, you should find answers to questions and learn new things in this collection of discussions.
Feel free...
It should never need to be said that a character needs a backstory. Generally, a story doesn't start with the birth of a character and end with their death (though it isn't impossible). The character needs to exist outside of the written story, to take part in the world and have an understanding the readers wouldn't have. Otherwise, the writer has to specify how it is the character knew how to hold chopsticks and what angle to bow to royalty, which would be no fun to read about.
Like any writing rule, there are exceptions. Many exceptions. Too many exceptions. There's a lovely description of a female character being taught how to dance in Amethyst of the Fringe by @AnnaKathrynDavis (which can be found in my Favorites reading list). It was fun and light-hearted, skipping over the detail of the feet and using it as a set-up for a dialogue section. That's brilliant. Its fine to specify those things as a fun detail, but not every aspect of a world as a lesson the character has to learn. If all nine mentioned dances in the scene were discussed in detail of foot placement and the history involved, we'd all bash our brains in. Hopefully the difference is clear.
What is the character's backstory? That is going to depend hugely on your world. A character backstory meant for a fantasy world should be wholly different from one meant for a real-world story. One can have dragons and one can't unless drugs were involved. As different as backstories should be, some elements overlap.
(1) Every character needs a goal. This should be an easy enough concept and included in both every story you read and every story you write. However, how you generate that goal is your decision. It isn't uncommon for main characters (and some lesser characters) to be introduced to their goal during the story, as a part of the hero's journey or a way to make the impact on the character more clear. Lesser characters and other main characters can come with their goals baked in, something that happened as a part of their backstories.
Villains almost always already have their goals and schemes in place before the start of the story or functioning in the background. Sometimes those schemes (like murder and whatnot) give rise to the goal of the "hero" or other characters.
Note that the goals should affect and drive the characters. Change drives character development, and a goal is a sure-fire way to change a character. Goals are also a fabulous way to create conflict. Recall Boromir from Lord of the Rings, a noble and just character who was charged with bringing the ring to his liege. He acted in ill because his nobility was corrupted, something readers and viewers were aware of from the first lines of Boromir and learned more about as the story went on (without Boromir). The conflict sowed the seeds of doubt that Frodo carried all the way to Mt. Doom.
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(2) Tie the character to the world, or at least a piece of your setting. Every character in a major fantasy should have a homeland, though it need not be mentioned with heavy emphasis. In an urban setting, at least one character should be familiar with the setting (good or evil) to reveal the details baked in so lovingly by you, the writer. Tying things in from setting also allows writers to mask later plot points as flippant backstory jabber. Imagine a character chuckling about a terrible, skeezy suitor to her friends abroad only to find later on that he's the villain behind the scenes, desperate to win the love of his greatest obsession. Imagine a warrior character indicating a massive scar and grimacing about who gave it to him, only for that character to come back and kill him or those he loves later.
