Does the fastest toon really determine who goes first?

From my experiences no. It's random but might favor those wit slighter higher speeds. When u finish one battle I've also noticed it someimes moves on to the next characters turn instead of resetting. I'm pretty confident in my evaluation because I have dooku at about 213 speed and the rest are around 100-160. Dooku doesn't always go first but he does get a lot more turns at that speed. His outside turn meter might be influencing my decision, but I still think it's good overall.

If you mean like actually go first in every encounter that I'm unsure of. I usually go first but maybe that's because I'm controlling it like a courtesy to go before the AI does? Might be a guess. I do notice that sometimes others go first but if it were truly random it be more along 50/50 while I feel I go first a majority of the time. Could deal with speed in that case.