1. Yes. Use good pad below - it will help make the floor more absorbtive at slightly lower frequencies.
2. I prefer sheetrock. It's better at isolating the room and also frees up the possibility to put more absorbtion scattered through the room in more effective places without overkilling the high frequencies. Whether you go with suspended or drywall, plan on filling the cavities totally with fiberglass or rockwool.
3. Cheap and soundproof don't go together - sorry. You can put a removable panel over the window that has 2 layers of drywall on the front and is filled with fiberglass. Leave a lip around the outside and weatherstrip the back. That's about the best cheap soundproofing you're going to do. As for the door, replace it with a solid core dore and get the edges sealed up. Consider a drop seal for the door bottom.
4. No need. If you run a dedicated circuit to the rack from the box and ground that appropriately, that will be fine.
5. If you can plan for it - sure. That will work fine for the bass treatments. Just understand that this means that those places will need to be sealed up and heavy drywall put on the back of the wall to keep sound from leaking in and out.
6. Plan, plan, plan. Consider everything together. Don't buy too big a screen - that's the biggest mistake people make. Figure out how many seats you want first. Put them in good locations acoustically. THEN look at the screen size that's appropriate for that seating distance that will also allow good speaker placement (not buried in the corners).
Don't forget to plan for cabling for things like IR repeaters, Cat5 or 6 for control, network, phone, masking systems, fan controllers, etc.
Also, run conduit everywhere! No matter how well you plan, something will come along that you didn't plan for or a new standard will come along that you need to rerun cable for, etc.
Welcome to the madness...