Should Yom Tov candles be lit in the Sukka over Sukkos?
Lechatchila, one should light Shabbat and Yom Tov candles where one is going to eat (Shulchan Aruch 273:7 and Mishna Berura there), which in this case is the Sukkah. However, the Talmud (Sukkah 29a) explicitly forbids keeping lit candles in a small Sukkah and this is codified in Shulchan Aruch (OC 639:1). The Mishna Berura there (sk 8) is clear that this doesn't mean the minimum possible Sukkah (7x7 tefachim) but rather any Sukkah which is small enough for there to be a risk of fire. If your Sukkah is such a risk, then you should light candles on an indoor windowsill or something adjacent to the Sukkah (where you can see them) if possible. If this is not possible, then you can light them inside but you must be sure to have them last long enough that you derive benefit from them at night (even after your meal); otherwise the brachot you said when lighting them were in vain (Shulchan Aruch OC 263:9).
Technically, yes. Candles should be lit on the Yom Tov or Shabbos table, or at the very least in the same room (unless there is a danger, such as young children who can get hurt). Succos would be no exception (barring any danger of course). Also, the Succah is meant to be like your home so everything important should ideally be done there (including, for example, davening, if you're not at shul).
I have seen many people who light in the Succah. One solution, which we do in our home, is to get special "outdoor" candles/candle holders that protect from the wind. They often use regular tea lights.
On YT, the candles can easily be moved, so they don't have to be left out there when no one is around (shabbos becomes more complicated and it wouldn't be safe to leave candles unattended in the Succah).
Oh, goodness, I would say no. Please, please CYLFC (Consult Your Local Fire Chief) before doing anything risky with candles!