Ido -
sorry for the delay - it was a busy week!
it is totally possible to use the TRF7963A here to read the ISO1444A tags as you say...the mux design is independent of the protocol. just make sure you tune your antennas with lower Q setting required for the ISO14443 cards in general.
running the thing from battery power - also should be possible, but within reason of course...what kind of battery and what capacity you need is something you need to account for.
the distance requirement also depends on the size of the tags and the size of you antenna - what sizes are you thinking about using?
tags are available commonly for ISO15693 and ISO14443A worldwide....i would recommend you use the largest ones you can.