Rename the PSN account

Content downloaded onto an activated console is accessible to all users on the same console as long as the console is activated with the owner of the content's PSN ID. Some content specifically prohibits this.

Content is not shared in the store across PSN IDs and only the account that purchased the content will have the ability to install the content. To share content across accounts, simply have the owner of the content activate the console on their account and install the content on the same console.

For content purchased prior to November 18, 2011, you were allowed to have that content on up to 5 PS3s, and content purchased after November 18, 2011 is only allowed to be installed and activated on up to 2 PS3s.

Sharing across multiple PSN IDs violates the TOS and some users have been banned for it.

One: You can back up save files and then restore them at a later time even to another account. If you are a PS+ member you can back them up to a server and they will be linked to your PSN. However in your case, you'll probably want to back them up manually, which can be done as so:

1. On the XMB (cross media bar), go to the Game section.
2. Go to Game Saves
3. Put in your memory stick (cf, ms duo, sd)
4. Find the game save you want to copy/backup, highlight it and hit the Triangle button.
5. Choose the menu option to Copy
6. Hit the X button on the memory stick and let it copy.

Source: PS3 : How to backup PS3 game save files to memory stick / sd / cf

It should be noted that some games use copy-prevention methods to, well, prevent copying. However, it's still possible to back even those games up. Google is your friend here.

Two: I'm surprised the previous owner's PSN is still on there, but yes you could use his DLC, as long as his PSN remains registered on the console (so don't delete his User account.) Off the top of my head I don't know how this will affect trophies. You should still be able to earn DLC trophies, but they might register for the owner of the original purchase. (The PS Vita has this problem.)

Three: The PS3 is not region locked for games, so you should be able to play everything fine. However, I do believe the Playstation Store is region based, and so some content will only be available depending on which region's store you access. I'm not sure if this is determined by the console (e.g. a US PS3 vs. a JP PS3) or registered PSN region. Also, you may have some conflict if trying to purchase content that is normally not available in your region.

I hope this helps!

P.S. Congrats on the new PS3!