Can i play FF Anthology, Chronicles and Origin on my PS2?? And if i could, do i need to get a PS1 memory card for my PS2 ?

FF Origin, yeah you could play that on the ps2, I've tried that once and it did work but the other two is a no no. The memory card thing? No idea

Actually, it's only the early versions of FF Anthology and FF Chronicle which were buggy, and glitched when run on a PS2. Square later corrected the bug, and re-released the games, but as far as I know, there is no real way of telling wihch version you have.

Incidentally, the European versions of FFVI (it was released on it's own in Europe) and FF Anthology run perfectly on the PS2 - it was only the US versions that were affected.

Yes, you need a PS1 memory card.