and are all LCD monitors compatible with a ps3?
No and No There are known hardware differences between PS3 and LCD's this is due to compatibility in HDMI versions that was released over the past few years bets why: New PS3 and New LCD's very likely to be compatible but read reviews and do some Google searches to confirm this
You can have both connected at the same time, but you won't be able to watch both of them at the same time.
Lcd Monitor With Hdmi Port
No, however most new LCD monitors have DVI-D connectors, and you can connect DVI-D to HDMI with a DVI -HDMI adapter or cable. Remember of course that you will need to make separate arrangements for sound.
