Yes you can.
You are supposed to fur it out first. - That means a thin wood frame, usually 1x4 on the concrete FIRST. - It is not customary to apply drywall directly to a concrete basement wall.
Not really a good idea. The water over time from the concrete will cause the board damage. If you use a good pad there is no reason you cannot lay the carpet over concrete.
No, you do not.
no
If the concrete is indoors, dry, and in good shape, yes.
Carpet is difficult to install yourself if you don't have experience. For best results, rent a carpet stretcher from an equipment rental store. For easier carpet installation, consider carpet tiles. These are squares of carpet with an adhesive back. Simply peel off the backing to expose the adhesive and place the tile on the floor. Carpet tiles can be installed over vinyl, wood or concrete. Special carpet tiles can be used outdoors on patios or sun rooms.
The engineered flooring can be either floated above or glued to the concrete.
The engineered flooring can be either floated above or glued to the concrete.
You don't put padding directly on a concrete floor. You have to frame out the floor, lay plywood sheets over the frame, probably want a vapor barrier as well. Then you can lay any pad and carpet you want. There are certain types of carpet that come with an attached foam padding that are designed to lay over concrete. If you think you want to just glue carpet directly to the concrete floor, check the mfg. warranty first. Most mfgs. will not honor their warranty unless they specifically state that it can be glued to concrete.
Over time they may, but if it's a relatively new floor, it shouldn't.
Normaly this is not repaired. Just floor over it.
Yes. The question is, is that going to be economical to do so. I suggest you consult an engineer.