1. Some people like having foreign Pokemon, purely for collection or aesthetic reasons.
2. UT Pokemon are more desirable because they have not been tampered with. Therefore you can shape it to what ever you want. Events even more so for collectors, think of it as a rare new game from 10 years ago compared to a one that was opened and played with.
3. Yes you can, though only Wi-Fi events unless you plan to travel to the country in question for the local events.
4. Some people like nicknames because it gives the Pokemon more meaning, some don't. It's personal preference really.
5. No, if you breed shiny Pokemon together it will still be the same 1/8192. Unless you are playing G/S/C, in which case the chances increase, though it's variable depending on the species.
6. They are considered legit by only some people. In
Trade Corner we allow cloned Pokemon to be traded as long as they are clones of legit Pokemon. However some people do not like them, be sure to ask them before trading!
7. Once again, some people consider them legit while some don't. Always ask the person in question before trading.
8. Headbutting trees only appears in G/S/C and HG/SS. Basically, some trees allow you to encounter Pokemon, while some will not ever contain Pokemon no matter how many times you Headbutt it. The specific kinds of trees are the ones that contain one kind of Pokemon that is not normally native to HG/SS and those Pokemon can only be found in one tree respectively.
Phew, is that it? I hope I answered your questions and gave you the answer you needed >.<
There are few different ways, glitch (on certain games), Action Replay, or Pokemon Editing Programs. Some people do not like clones because they view them as hacked or cheated.