You don't use a PC to get games from the PSN, there might be some free games released on it sometime, like Treasures of Montezuma: Blitz on PS Vita.
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Yes, yes. You can either buy Ultra Mini Discs or download games from the PlayStation Network directly from the PSP.
Yes, you can play PSP games without a memory stick. However, if you're playing games from PSP UMD's (little PSP games in cases). If you want to play games saved in your PSP's hard drive, then no. So, pretty much by UMD, you can play games without a memory stick in your PSP, but you'll be unable to save.
There is a emulator at http://www.emulator-zone.com/doc.php/psp/ you will need to have the game files on your computer. there may be a program that gets the games off your psp source : i found out about emulator zone on tinkernut.com
you can get themes from games and your computer/laptop. games=completing levels,missions,goals,set of levels. computer/laptop=get the picture on your computer/laptop then connect the PSP to the computer/laptop and put it in the PSPs memory.
Download PSP Games for free here: http://www.pspisogames.info also, for torrent downloads try: http://www.mininova.org/