(adsbygoogle = window.adsbygoogle || []).push({}); Do I update the game to the latest patch befor I back it up?

I would update then do a backup. Doesn't really matter but the latest patch would probably add some better performance (speed)

It depends upon the game before you update it. Remember most of the latest updates will be for 3.60+ , and then your game won't work.

but if you do update and your game does not run, then just Delete it from GAME DATA in XMB

But no you don't need to Update games before you back them up.

You can check out the updates on the 'PS3 Compatiblity list' or check out Game Updates at Brewology - it tells you what updates there are and the Dates beside them