If you have a PS3 you can put videos from their onto your PSP and it should solve the resolution problem. If not, you will have to find some kind of program.
Games that will give you a lot of time for your money. I will explain why each gives you a lot of time too:
Jeanne D'Arc (this game is just plain long cause its an RPG, but it really never gets repetitive. Probably one game on PSP that just about everyone would recommend)
Crisis Core (the story itself isn't super-long, but there are TONS and I mean TONS of side missions which allow you to get all kinds of new stuff for your character. They can get a little repetitive though, but if you play it on hard they are quite a challenge)
Castlevania: Dracula X Chronicles (This games includes Symphony of the Night and the original Rondo of Blood (the game that is remade), so you get 2 and 1/2 games for the price of one)
Final Fantasy Tactics: The Lion War (Just plain long with a ton of character customization)
Disgaea: Afternoon of Darkness (this is a phenomenal game (arguably the best SRPG I have ever played) and it also happens to be the longest game on this list. You could easily log 1000 hours on this game, and I am not kidding. You still would have a lot to do after playing 1000 hours is the scary part...)
We had two bags of grass, seventy-five pellets of mescaline, five sheets of high-powered blotter acid, a salt shaker half full of cocaine, a whole galaxy of multi-colored uppers, downers, screamers, laughers…Also a quart of tequila, a quart of rum, a case of beer, a pint of raw ether and two dozen amyls. The only thing that really worried me was the ether. There is nothing in the world more helpless and irresponsible and depraved than a man in the depths of an ether binge. –Raoul Duke
It is hard to shed anything but crocodile tears over White House speechwriter Patrick Buchanan's tragic analysis of the Nixon debacle. "It's like Sisyphus," he said. "We rolled the rock all the way up the mountain...and it rolled right back down on us...." Neither Sisyphus nor the commander of the Light Brigade nor Pat Buchanan had the time or any real inclination to question what they were doing...a martyr, to the bitter end, to a "flawed" cause and a narrow, atavistic concept of conservative politics that has done more damage to itself and the country in less than six years than its liberal enemies could have done in two or three decades. -Hunter S. Thompson