Yes, yes, no, yes.
I hope this helps you.
Sorry, am feeling puckish today - must be too much coffee...(puckish is a Canadianism - see Hockey)
Yes, you can download Platinum from the DVDFab.com website (and purchase a new key from there, also).
Yes, you have to purchase a new key (your Gold key only works for that edition)
No, you had a free trial with gold, don't think you get another one with Platinum, as the only change is a couple of features, and you already know how to use the program.
Yes, a clean uninstall and a fresh re-install is recommended for maximum chance of dodging errors.