transfer photos from computer to Cruzer flash drive?

“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.