No, FlashBack does not have any options to automatically launch on Windows startup.
While you are recording, FlashBack will need somewhere to temporarily store your recording. By default it will be C:\Users\\AppData\Local\Temp\FlashBackTemp\.
Your recording will be deleted as soon as you click the Discard button so it is not possible to recover it if you click the Discard button by accident.
FlashBack has separate installations for each edition to allow users to install different editions side-by-side on the same PC.
When you next start either FlashBack app, your existing trial licence will automatically be updated to a full licence so you do not need to do anything.