It depends on how big the game is and how big your memory stick is.
You can install a game on your memory stick just like you would on a hard drive. when you are installing the game just choose to put it on your memory stick.
If you want to save the actual game (not installed) You will need to make an .ISO file (or a similar format) Programs like Record Now and Magic ISO can do this.
Chat with our AI personalities
When you download a game from the PlayStation Network, they are stored on the PSP's memory stick.
Yes as long as you have the memory.
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.
It has a small amount of internal memory, but you need a memory stick before you can save games.
You can copy games from one PSP memory stick to computer and then copy to another PSP's memory stick. Make sure you put the game on the folder 'GAME' on the memory stick.