Screen Sharing - basic questions

This will work for you just dandy. I have my G5 set up this way and although I had to jump through more hoops than you will, it's great. Additionally, a close friend has a Mini (older model, even) connected exactly the same way with no issues. Go ahead and get it all set up - all you'll need is an adapter from HDMI to DVI for your tv. Your Mac will actually recognize your TV as its monitor and choose the closest resolution. Note one thing, though- TV resolution is not native to computers and you'll either clip a little (like I do) or you'll have a black border on your display. Neither is worth worrying about and all video, web, etc display great.
I connect to my G5 (which has no keyboard or mouse of its own) via screen sharing to control it and yes you can see both at once. I find no speed issues at all. When your TV is on cable you'll have free reign over your Mini via screen sharing as you'll be using a separate input for your Mini as you do for cable.
Check here for creating a link for sharing when the time arrives.
http://ianmaffett.wordpress.com/2009/05/19/os-x-screen-sharing-link-on-desktop-or-dock/