1) Depends on where you live and who you're talking to. It's a really widespread beginner myth that 'ore' is almost never used. It's common, as well as boku. To the point where I was reading something where someone didn't know who was texting her phone, but the person used watashi, so she assumed it must be a girl.
Anyway, you don't use it in formal situations.
2) For handwriting? Handwriting doesn't have a lot of relation to computer fonts. It's pretty squiggly though. Here's a random site I just pulled off google:
http://www.yamasa.cc/members/ocjs/kanji ... enDocument
3) The same pronunciation of a word with different kanji involve different nuances. In some cases it's just nuance, but in others it's blatantly wrong to use a certain kanji in certain places. In your particular case, 上る is the most common, and is often used in the other instances as well. But uniquely, it's more focused on just going up places in general. Including up a hill, up the river, etc. 登る involves more climbing. Trees, mountains. 昇る is more of an 'ascend' idea. It's use for the sun, for example.
All words that have multiple kanji that are
common are like this. Some have alternate, rare kanji that don't actually change the nuance significantly. For example, I've never gotten a straight answer on the difference between 噛む/咬む, and I'm not really convinced there is one. The word is usually written in hiragana, anyway.
4) There isn't much reason to know. You could study it if you're simply interested in the etymology, but don't expect it to help you understand modern use. These things have been around for thousands of years. It's, what, the oldest writing system? And the Japanese only borrowed it, and then screwed it up - over the course of more than a thousand years. The etymology just isn't very strong anymore.
Either way, I don't have any specific references for you, sorry.