1) No. I just leave them on their original stands despite the height and size difference. Stands cost a bomb (3k+) which isn't really surprising as people shell out as much as 8-15k per monitor (multiply that!), but you can always try making your own if you're reasonably crafty.
2) I made my own desk as my old desk couldn't fit my two monitors and subwoofer. Before vs After. Remember you live in India, so you can easily get a reasonably good desk made to your size and specifications for as little as 5k.
3) By using whatever input is left lol. Most mid-range and upwards gpus have 2x DVI and 1x hdmi at the very least which is more than enough for 3 monitors. Connect two monitors with DVI and the third with a HDMI to DVI cable and you'll get display on 3.
Sorry I don't know much about stands aside from knowing that they are very expensive. Perhaps someone else will help you with this.
Apologies, I thought I had uploaded pics of my desk. Heres what it was and heres my current arrangement. This is a old pic and not what it currently looks like, but I basically made the desk with plywood so that it could comfortable fit two monitors and subwoofer and also integrate my system into the desk. I guess you can make a far better and more flexible desk just for your system if you used a carpenter.
Theoretically it should work, but theres always a chance that it won't. My 280x runs with the hdmi plugged in but it often blanks out and reconnects after a few seconds which is slightly annoying.
Thanks for sharing man, your desk looks great! Unfortunately I have no talent when it comes to working with wood