No, you shouldn't need to re-download all of them as you discovered. You only have to force the system to refresh it's licenses. When you download any of the free PSN+ content, it automatically stamps that content with an expiration date that is the same as your subscription expiration at that moment. When you extend your subscription, it doesn't update all of your downloads immediately.
But, if for some reason you do re-download a title (even if it's one you've previously deleted). All of your game save data should still be present on your PS3 as save files are stored independent of your content licenses and software downloads.
Oh and one other note. If for some reason you let your PSN+ membership laps, you could permanently loose some of your previously downloaded free games. I have seen that there are a number of titles that remain free contingent on a continuous membership.
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
As been stated before, you are not able to use the same account on multiple systems simultaniously. As soon as you log in on another system, the other will log out, because each account has an ID and that ID can only be online once. Else you can't who actually is using the account.
If you want them all to play together you have 2 options.
Pay for multiple PS-plus accounts as well as the games. (This is the only way they can all play online)
Find a game which supports multiple players on 1 console. I can't tell you any new games which support this (split-screen), but on PS2 there was Need for Speed and FIFA if I remember correctly.
For your information, pretty much any system (PC, XBox, PS) only allow every account to be logged in once. Don't get your hopes up and try to get around this. Unless you violate the ToS there is no way you can achieve what you want to.