Plastic sheeting works well for this, and yes it goes behind the drywall on exterior walls to help prevent moisture from getting to the drywall.
No, but it should be securely covered by heavy canvas dropcloths.
Drywall primer should be used.
A vapor barrier is an impenetrable layer that keeps water from seeping through from the ground. It is always advisable to use a vapor barrier regardless of humidity.
You can install tile glue right onto drywall. However if you are doing this in a bathroom, first consider all the advantages of using concrete/ fibre boards around the tub and shower. They are far more water resistant, made for tiling, easy to work with and come in handy sizes 30x60 and 36x60. - I have used this in preference to drywall for over 10 years and never had an unhappy client.
Drywall anchors should be placed no more than 16" apart. On a 20 foot wall you should place approximately 15 drywall anchors.
No, the prime coat can go on anytime.
Ratings for drywall contractors in Houston can be found at homeadvisor, angieslist and linktown for example. One should always consult an expert before taking any decisions.
tape, float, sand, re-float, re-sand. . .then prime
Yes, it should
You will be very careful when you deciding for the drywall color. You should not check the color when there is too much light shining on the wall. After that you can find color you want for your drywall repair.
Install first,then delete.
You should never anchor a wall arm like this into just drywall. It is very dangerous. You will need to find a wall stud under the drywall to anchor this into.