I don't think I started showing until four months into pregnancy, had a very cute bump for a while and now of course it is a pretty big baby belly! I've heard from lots of people that you do tend to show quicker with babies 2 and onwards (this is baby 1 for me). To be honest I noticed my hips getting bigger first and then my belly caught up!
We heard baby's heartbeat at our first MW appointment and that was at bang on 12 weeks, but she did have to move the Doppler round a bit to find it and true often you can't hear them. It is cool thought the first time you hear it and you can hear baby moving and grooving around too