MP4 with a special CODEC (google it). Telling you the exact codec won't help you as you need a converter that supports it. You will need a proper video converter or a video that specifies it work on...
You can't download videos onto your PlayStation Portable from your computer. They make videos specially for the PlayStation Portable that are in almost the exact same case, but they will have a movie...
You can't, unless you have custom firmware, if you do, then you can use psptube. You can download videos from your psp... either from the PlayStation store or RSS Crackle feed.