A GIGAHERTZ?!?!?!?!
Fix your computer. Now.
I know for a FACT that a 500MHz machine with ZSNES on it and a video card with adequate RAM(16 is enough, 2 isn't)can run any non-SA-1 game at the full 60 FPS with a graphics filter applied.
As far as emulators...
ROMs are legal. ROM images are legal too, as long as you make them yourself(or as you mentioned, they've been made freely distributable, as have Vectrex ROM images and the Jaguar BIOS ROM image).
But that's not relevant to a discussion of PS2 emulation, as PS2 games don't come in ROM carts, so the only PS2 ROM is the BIOS.
And no, there is no decent PS2 emulator yet.
There's not even a decent Dreamcast emulator.