So, 네 is like an abbreviation of 너의. 의 is used to show property kind of like the english 's. So that is fine to say, but as you mentioned, that is used in casual language or 반말. 당신 is a polite way to say you, so you could say 당신의 생일, but it might sound a bit stiff. A lot of times the word "you" is omitted since you can usually tell by context who's birthday you are asking. For example, 생일이 몇월 몇일이에요? If you are talking directly to one person, what are the odds you are asking your own birthday? So they often omit words like "you" or "I". Hope that helps.

"Yes, it is interesting. Kanji is difficult, but Hiragana is not very difficult."

I would say as many hours as you can stomach before your brain turns to mush. :P If you mean actually talking to another human though, I recently tried something new that I quite like. I have another Japanese learner who I meet with once or twice a week and we decide on a grammar point or topic ahead of time, and we promise to stick in Japanese only. It takes away the anxiety, and gets us in the habit of communicating in only Japanese. I've not been studying long, but I find that we stick in Japanese for upwards of an hour each time and I have loads of fun coming up with funny sentences and seeing what he comes up with as well. :)

You can say "I will switch off the light" or "Please switch off the light", but it sounds more natural to say "I will turn off the light" or "Please turn off the light"

Both work. You can say "I love to fish." or "I love fishing." You can even say "I love to go fishing." All three of those are correct and common English. :)

Bile refers to stomach acid. Have you ever vomited on an empty stomach? That yellow liquid is bile.