1) I believe so. In fact, some candidates who failed to get through on their first attempt were successful on their second. As far as I know quite a few of them tried through the same FTO.
2) If you had attended the selection day at FTE then I'd say you'd stand a better chance of making it through to the final stage by going there again; than by changing FTO (purely because you'd have experience of what their selection was like). However, as you didn't make it that far, I doubt it'd make a great deal of difference which one you apply to on the next occasion. In fact, I've even heard it mentioned that it's BA who decide who to invite to each of the FTO selection days based on the online applications, and if that is the case then it won't make the slightest bit of difference which one you apply to.
Hope it's helpful.
