1. Should I install only redhat packages into redhat system?
In general yes, you will find that for any packages other than extremely simple ones you will hit big problems with this. If there isn't an RPM for your version of your distro, compile. Others MIGHT work, but they might not.
Rules of thumb:
RPMs built for earlier versions of your distro in the same major series will normally work, ie 7.2 RPMs will install OK onto 7.3 but probably not 8. 8->9 is special because 9 is really 8.1 except for NPTL threading, but that only affects a few packages (java,wine,realplayer spring to mind).
RPMs for other distributions probably won't work, but if they do try and get the one that matches most closely with your version, ie MDK9.1 for Redhat 9, SuSE 8.0 for redhat 7.3 and so on.