“first, is this a good idea (in other words, is it safe to put it all on a flash drive and have that as my only backup )”
If you delete the images from your hard drive than this USB drive is not a backup, it’s your sole keeper of your files. So, when the USB drive fails, and all things fail, it’s not a question of if but rather when, you will loose all your photos. If that is acceptable to you then yes this is a good idea.
If you want the photos off the pc and backed up then I suggest copying them to 2 or more USB drives. That way when one fails hopefully the photos can be restored from one of the other devices.
" delete them from my computer so i will have more space and hopefully a faster computer…"
More space yes, faster computer, highly unlikely. A defrag of the hd would be more useful.
“second, how do i actually make the transfer???”
Drag & drop using Windows Explorer works. And I’m sure there are photo apps that will do the transfer also.