These days as long as you are on 3.55 or below you can install PS3 Custom Firmware (CFW) such as:
There are others, but those are the most popular at the moment. Be sure to follow the guides on how to backup your flash and dehash as a precaution before doing so if you go with the 4.xx CFW's above.
As for going online, you can but it's a giant risk so even with apps such as Stealth multiMAN in the end only Sony knows what they are looking for (which they can change at any time) to Ban PS3 Consoles
meaning you would have to take yet another risk attempting to UnBan Your PS3 Console
which is not an easy task either.
Long story short, if you game online have a second PlayStation 3 for offline/backup/homebrew use to be 100% safe.