First of all - since RTSP is a protocol with no defined standard codec - ensure that you have the correct codecs on your computer to decypher the stream when you have received it.
Onve you have managed to get your hands on the codecs, there are loads of freeware and open source RTSP capable media players - VLC Media player for instance
Regarding yoru wish to record the feeds in real time - again, a program like VLC has "save/convert" functionality which can capture a network feed from RTSP and save in a format to your PC.
Lastly, the aforementioned (sp?) software also supports opening multiple instances... as do many other media players which fulfill your criteria.
Ben