Ps3 – Viewing Yorda’s subtitles

Original PS2 and PS1 games running on the PS3 (this applies both to the disc versions and the downloadable versions from the PSN store) save and load to virtual memory cards on the system. If you use the adapter on your original memory cards, they'll transfer into these virtual cards and be usable by the original versions.

Remastered (i.e. HD) versions of PS2 games, however, use the PS3 save data format, and don't access the memory cards at all. So unfortunately, no, this won't work.

All PS3s are capable of playing PS1 games, whether they are on disc or downloaded from the PSN.

Only some earlier fat PS3 models can play PS2 disc-based games.

Recently though, Sony have begun adding "PS2 classics" to the PSN store, which are playable on all PS3s. They appear to be using a full software emulation to play these games.

Presumably they have been tweaking the emulator on a per-game basis to ensure that each game runs correctly. (The partial software emulation on the CECHCxx and CECHExx PS3 models was decent, but many games had small glitches.) There is only a very small selection of PS2 games available on PSN at the moment.