I just received my PSP 3000 I bought online used and the previous owner included 3 PSN games he bought with the purchase (flow, Super Stardust, and FF 7). I want to know if I can transfer these games to my PS3 or at least just FF7

I already tried connecting a USB cord from PSP to PS3 and seeing if I can copy the games but I couldn't find such option, im guessing I have to use remote play? I haven't made an account yet on my PSP because I don't know if i'll lose the games if I do so

You can't, because those games will be locked to his PSN account. You would need to put his PSN account on your PS3 and then download them

if I make an account on my PSP though the games won't get erased right?

They won't be erased, but beware of DRM. The game "belongs" to your seller ID. If you change it in your PSP, you won't have the rights to start it up. The only way to earn them back would be to enter the sellers PSN ID again.

well this is what I want to do

I want to transfer the PSP demos I downloaded off my PS3 (MGS Peacewalker, Socom FTB3, Monster Hunter) to do this I believe I have to have my account on the PSP

what exactly should I do to keep the games on the PSP and transfer the demos to my PSP

It's a large pain to do what you want to do as it involves switching between PSN IDs on your PSP.

This is a pain AND it requires the previous owner to give you his PSN ID info which he probably won't do.

Just kiss those 3 games of his goodbye as they are "his" and only for his PSN account. In all seriousness those 3 games are maybe like what $20? If you want them, man up and pay or if the previous owner had the "3 games included!!!" as a selling point, ask him for the price of the 3 games back since you can't use them.

I'll give more explanation here.

Games purchased on the PSN (currently this is how their DRM works) you can have up to 5 PS3s and 5 PSPs all "activated" on the same PSN ID. Any game bought from that PSN ID can be used on those systems as long as those systems are still activated under the purchasing PSN ID.

A PSP can only have 1 active PSN ID on it at a time.

Thus, if you, using your PSN ID on your PSP any game that is on the PSP that was downloaded via another PSN ID (and thus locked to that PSN ID) you cannot play unless your PSP is activated on that PSN ID.