I'll give you the basics now.
1. If you are basically fluent then yes, you can think in either language.
2. The language you naturally think in depends on which language you feel closer to and the situation. E.g. if you live in UK and are surrounded by English people, you will think in English. If you go visit France and are surrounded by people speaking French, you will switch to thinking in French.
This is simply because some words don't have translations or cannot be interpreted the same way so it is easier to respond if you are thinking in that language. So our brains adapt and switch.
3. Yes, you can willingly switch between the languages you think in if you want.
4. The age you learned the language does not really matter, it is the level of fluency which matters. Obviously, if you learned it at younger age, you will probably be more proficient in it compared to a language you started learning 1 year ago.
Interesting facts:
1.The accents people have while speaking a different language appear mostly because the tongue and mouth are used to certain movements. That is why people from the same country have similar accents. Example, Russian language is, what I like to call, a hard language (as in, hard in the sounds while French or English have pretty soft sounds). So when Russians speak English, they are used to the hardness and harshness of Russian and find I hard to add the softness that English requires.
2. The more interesting thing to investigate is how speaking in different languages affect personality. There have been studies that the same person speaking in one language may act more polite, change their tone of voice to a higher pitch. And when speaking in another, they will act harsher and change their tone to a lower pitch.