A HTPC case generally looks more like a large audio component like a large amplifier or receiver than an actual PC case. At least the ones I've looked at.
Other things would be a possible remote control, maybe a small mono LCD display that can show some system info. More expensive HTPC ($500+) cases have a small 6" or 7" 800 x 600 resolution display that can be used to display lots of information and can be used while installing Windows so you don't need to connection a monitor. Some of them may be touch screens as well.
It's all about aesthetics. It still operates as a PC.
My HTPC was built around the SilverStone Crown CW02B case back in 2008 and it currently sells for around $375.
This is an example of a HTPC with a built in color LCD display if you really wanna spend a lot of money. That's the SilverStone Crown CW03B and the screen is 1920 x 1080 resolution.
Yes. It's just a case after all. For now I simply have an evaluation version of Win 7 installed to make sure Win 7 is fine with some programs that's on my primary PC before I switch over from Win XP to Win 7.
I am considering a HTPC front end that acts like a media center that's used to browse thru movies and music stored on the HTPC. And of course play those media. XBMC is just one of many examples.