I would suggest copying the data instead of moving it and then later using
clean_transmission to get rid of it when you're done seeding. I know with Deluge you can use the Flexget plugins to update torrent settings at some point after loading them. I don't use Transmission, but from reviewing the available plugins I don't think there is a way from Flexget to change options (such as download path) after the initial loading of a torrent. I could be wrong about that, though.
Regarding your second question, Flexget isn't magic. It does pretty well at figuring out what stuff is supposed to be called once it knows the media type, but distinguishing between TV and movies in the same task, with no hints for it to look at, would be very difficult if not impossible (due to series named the same as movies, special episode titles of TV shows that can look like movie titles, etc).
I would suggest putting your downloads into separate subdirectories initially (i.e. /downloading/files/tvshows and /downloading/files/movies) and then moving them appropriately, or using content renaming to give movie files a name like My Motion Picture [movie].mkv and then have your task look for [movie] in the filename to determine whether it's a movie or a series. (The
move plugin can rename files while it's moving them, so you could remove " [movie]" at that time to get it out of the final filename.)