You don't, you buy a memory stick and put it into the slot on the left of the psp - near the wifi button.
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Bad blocks is detected on first 1023 sector of the internal memory card. No remedy on it unless you are capable of replacing the NAND chip in PSP go and transfer the NAND data from your broken NAND to a new Working NAND chip (NAND chip had unique system files required for PSP Go to boot, you cant use any other PSP Go's NAND data as they have different key sets stored on each PSP) Be warned that System Memory might be in pinch as the memory card goes bad, the system memory area may get damaged too and may cause software brick and your PSP Go is good as paper weight after that.
They are both the same thing as far as the PSP is concerned. When the game finishes downloading from the PlayStation Network, it is there on memory stick and ready to be played whenever. There is no formal 'install' procedure like for a PC game.
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.
You will need a memory stick for ALL things you want saved on the PSP.
The psp 1000 has 32mb of internal memory while the 2000/3000 has 64mb.