I am leaving in mid-January for 4 months (January through May).

#1: Should I drain the pipes in the well water system and shut off the pump at the main electrical box?

#2: Would draining the X-Trol pressure tank damage the unit (ie. Affect the bladder)?

Yes, you need to drain the complete system, even any water that may be in the pressure tank (shouldnt be much water in the pressure tank to drain). Anything that has any water in it and is likely to freeze, needs to have the water removed. Also, get all the water out of the toilet tank and bowl. Add some RV antifreeze to all traps and toilet tanks and bowls. Just a cup or two for sink traps, and just enough to keep the flapper wet in the toilet tank and enough to fill the integral trap in the toilet bowl (to keep sewer gasses out) Don't forget any floor drains, washer standpipes, etc.

If you really want to be sure you come home to no issues, you may consider hiring a plumber to come winterize your home for you with the understanding that they will stand behind the job.

PS. Common things that get overlooked on winterizing a home include water softeners, washing machines, dishwashers, fridges with water for icemakers and drinking water, reverse osmosis systems, even water heaters, etc, etc.

When I winterize a home, I use a commercial air compressor and literally blow the system dry. It may seem a bit overkill for some jobs, but I stand behind my winterization. Having it done professionally will let you enjoy your time away that much more with peace of mind. Take care, and good luck.

PS. Common things that get overlooked during a winterization are water softeners, water heaters, washing machines, dishwashers, fridges with water option, reverse osmosis systems, etc, etc.