Want to buy a mid range AV Reciever model, but my concern is that can I provide input audio from another room(away from 30feet) by coaxial cable (or only RCA audio cable required). 2nd, for output can I use coaxial cable (30 feet) for bathroom (without amplifier) without any qauality compromise.
RCA audio cables are normally coaxial in construction, and are fine out to 50 feet or more, normally. I've run 100+ feet when needed for auditorium A/V setups. While there are fancier ways to go long distances, with modern equipment and cables there's little need for them in most cases.
Most coaxial cable is not particularly suited to use as "output, without amplifier" - ie, speaker cable use. Use speaker cable for that job, it's what it's made for.