Just unlock all the characters, no hard mode necessary :)

i recommend the GVUSB2, its fairly cheap at about $35 and if youre using component for ps2, i think the avermedia LGP has component input.

it all depends on what cables you use, a GVUSB2 for composite or S-Video, or an Avermedia for HD component. for the GVUSB2, you could get splitters, but i think you would be fine with plugging it into the capture card, then use AmaRecTV into OBS (for streaming) and play off the computer/laptop. i dont own either of these capture cards though, so i cant really give you much more info. but in the meantime, enjoy speedrunning the game dude :)