The standard distance that cabinets should be installed away from where there is a doorway is 4”. Using this measurement will allow enough room for door casing to be put around the opening. If you’re working on a house remodel, then you can make the dimension more like 2” from the molding that is already around the door. read How Far Back From Doorway do Cabinets get Installed

Although it’s not recommended, drywall screws will work for installing cabinets. You just have to make sure that you pre-drill a pilot hole in the cabinet part that you are attaching to either the wall or another cabinet. If you don’t create a pilot hole, there is a good possibility that when the screw is sinking it can snap off. These screws do not have a high sheer strength. read Can Drywall Screws be Used for Cabinet Installation