Hi Borsuk and welcome to the awesome mage class :) I'll try to answer all of your questions in order, but I am not that very very experienced, so don't trust me to 110% on everything :)
1. You can identify a twink by his level, which usually is 19,29,39 or 49. The rest tend to level to 70 or so. Also, you can target them, then right click their portrait/avatar and select Inspect. If they have absolutely awesome gear with many enchants and rare/epic stuff, they are probably a twink.
2. I would avoid going to battlegrounds at least 10-29 because there are a LOT of twinks. Also, in my opinion the higher level PvP is more fun, as every class can take advantage of all or most of their specific spells/attacks.
3. I would say they're idiots, have never encountered this myself, only higher level people.
4. Well...depends on your level but use every trick in your ******* and be creative :) It all depends on the class you are meeting, but that matters more at later levels. If you want to ask about a specific class, PM me!
5. No, they can not steal any items. If it is duels, the winner just wins the battle and nothing more. If it's battleground PvP, they can steal your "Insignia" from your body, making you unable to resurrect at your corpse, and making you wait the 1-30 seconds at the Spirit Healer, which is what you usually do anyway. They also get a very small sum of money from stealing it.