Second question, an lcd monitor will work with ps3 if and only if it is HDCP-compliant. A non-hdcp monitor with component input might work, but I imagine that's not your monitor. So check the specs for HDCP compliance.
No there aren't slots for the PS2 memory card but there is an adaptor you can buy for 15 bucks to transfer over all of your saved games to the hard drive.
And yes, HDMI is HDMI, if the port is there, it will work.