If you are unsure of yr power usage and are on a tight budget get the ITPS and an inverter, will save you a lot of time and with some common sense it can work just as well (often tank batteries will be useful here).
As for placement, i've gone the head unit route but if you cant find anywhere else to put yr screen then yes you will need an amp. A 2 channel amp that is 2ohm stable will be ok, most factory speakers are 4ohm, but itll be worth checking. Or you could just get a 4 channel amp.
No, you dont want that monitor, for decent picture go VGA - lilliput or starvision or xenarc.
If the dvd player is a slimline laptop one then im sure you could find a place to cut out a hole, theyre tiny.