Hi Cyanonly old model will have a firmware bellow 3.55 (like PhatPS3, or slim up to the PSMove Demo disc pack, released near September 2010)
If on of these console have a firmware past 3.55, there's a way to downgrade them using a hardware NOR/NAND flasher (but it requires soldering skills).
Newer consoles can't be downgraded at all.
You will have more chance to buy a used PS3 already hacked than finding a new one on an old firmware.
Backups used to depend on the firmware you used. New games had new encryption key which required patches to play on old console firmware.
But it's now possible to install a custom firmware at the same version than the latest official firmware (4.30/4.31) so the games don't need patches anymore.
If a game is not working, it's because it's incompatible with the gameManager and/or launch method.
You can see a list of backup compatibility here: http://www.pshomebrew.net/wiki/PS3_Backup_Compatibility_List
Some game haven't been tested yet.
Other games are marked as not working, but it might be an old report because there's no precision on which cfw/Manager it was tested on.
thanks for your answer
as you said it is possible to install CFW 4.30/4.31 but the current guide is based on CFW 3.55 and I heard here and there that 3.55 is the best as you might not be able to downgrade above it(unless you use an E3 flasher). so how do I play the newer games if I want to stick to 3.55?