Sheetrock is a brand name for drywall, a panel made of gypsum plaster pressed between two thick sheets of paper. The terms are often used interchangeably.

Minor repairs can often be done by homeowners, but significant damage may require professional repair to ensure a seamless finish.

The cost can vary alot based on location and especially the size of the job, but typically ranges from $1.50 -$2.00 for new homes to $3-8 per square foot for remodels. Any Jobs smaller than a bathroom is bid by how much time and materials it will take instead of sq footage. Typical minimum is $400

Too much mud over the tape causing humps. butt joints not feathered out enough. screws not set properly. short choppy strokes on inside corners. scraping popcorn and painting without oil priming the dusty ceiling. Putting joints in high stress places like the corners of windows or above doorway corners. Paying a contractor more than the cost of materials up front, Hiring the guy with the lowest price. Not looking into the contractors work history or reputation. Hiring a drywall contractor that shows up in a car(where does he put drywall sheets?)

Too much mud over the tape causing humps. butt joints not feathered out enough. screws not set properly. short choppy strokes on inside corners. scraping popcorn and painting without oil priming the dusty ceiling. Putting joints in high stress places like the corners of windows or above doorway corners. Paying a contractor more than the cost of materials up front, Hiring the guy with the lowest price. Not looking into the contractors work history or reputation. Hiring a drywall contractor that shows up in a car(where does he put drywall sheets?)

Showing up in any vehicle other than a truck or work van. when potential contractor leaving walk him to his vehicle and glance in the back of his vehicle, does it have signs of drywall work like stilts, t-square, bucket of mud, white dust from drywall? google his company name and personal name, what do you find? should have some online presence.  Ask for a list of references, the more he provides the better. Call at least 1 picked at random. If you don't see a lot of signs its a decent business don't pay money up front, offer to purchase materials instead. (pay supply house directly) When he starts hanging are sheets snug and are cuts straight? When he starts taping compare it with the images on my website should be neat and clean edges. 

You can if the paint is self priming. Otherwise use pva drywall primer to seal the board first.

Yes 1/4", 3/8 or 1/2" drywall are commonly installed over plaster and popcorn ceiling texture and stubborn wallpaper too. Just make sure you mark the joist or studs and use screws that are long enough to penetrate the wood at least three quarters of an inches.