Did you activate the special game fixes for MGS (I gather you are still using SPUEternal)? You might want to fiddle around with the buffer size (smaller means less lags, but more stuttering - try to find a compromise).

To get the ePSXe main menu back, press Escape. Saving states was F3, IIRC and loading them was F5, although I recommend using memory cards, instead. Save states can break things, you know.

Playing a different game means restarting ePSXe. There's no way around it.