Acutally you can; my brother is doing it with a friend, but it's tricky. It's like buying plus, having your account on both devices and interchanging devices with someone else.
Take: Skynet (my brother's PS4), and Cerebro (his friend's); Charlie (my brother's account) and David (his friend's).
There's an option in the PS4 that says something like: "Activate Device" for "Game" and for "Video", to activate a main account on the device.
David has Plus privileges on his account but his 'Active Device' is Skynet, and vice- versa Charlie has Cerebro as his main device. And they both have their accounts on both devices (main and secondary).
So on Cerebro are both accounts, Charlie and David. Charlie is the main account of that device but it's on David's house; and on Skynet too are both accounts, David is the main account, and it's in Charlie's house.
Basically David+ is playing with his account on Charlie's device, in his own house (as if he were a guest in his own device), and Charlie is playing in his house, with his account on David+'s, device.
Cerebro (in David+'s house): Skynet (in Charlie's house):
> -Charlie (Main) -David+ (Main)
> -David+ (2nd) -Charlie (2nd)
This way David+ can play online on Cerebro and on Skynet, because his account has plus, and Charlie can only play online on skynet because the main account of the device has plus and enables all accounts of the device to enjoy the plus privilege of online play.
And yes: anyone of them can buy a game and download/play them on both devices.
Best Answer
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:
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!