2) HDMI carries both digital video and audio.
3) If you have a lot of components with HDMI out, then it is nice to have a HDMI switcher, or a receiver that can combine those, and then send just one HDMI cable to the TV. In my case my DVD player is the only thing, so I just run it directly to the TV.
4) I'm sure your TV has component inputs, nothing wrong with that, component still gives you a great picture. Not sure what your meaning when you say "can't watch movies properly" If your DVD player is 480p progressive scan there won't be a ton of difference in the picture of HDMI versus Component. I have a 720p/1080i upconverting player and I do notice a difference via HDMI compared to 480p component.
5) My room is bigger than yours and my 60's do fine.
6) That is your choice, probably depends on your budget. I love my Denon 2805, does everything I need for now.