Not buying the everybody in the house is so greatly affected by the drywall dust. It causes short term, very short term issues. Drink some water. flush your sinuses with a Neti pot if you are having some issues. I work in construction and am around drywall dust quite regularly. I know a lot of drywall tapers/finishers (those are the guys that make all the dust). It is for the most part not a big deal. I can understand with the asthmatic child as they react very differently than a healthy person so I will not discount how he was affected.
but here is what you do:
wash clothes, curtains, and anything else that is soft and cab be washed. You clean the home just as you would when you have dust. Shampoo carpets if you feel the need., Then you will have no drywall dust to worry about.
since it appears money is tight and transporting the clothing and such to the laundromat so here is what you do:
take the clothes, bedding, whatever, walk outside with it and shake it in the air to remove most of the dust. Shake until it quits giving off dust.
actually toilets DO mount to the pipe under them and may or may not sit firmly on the floor. .
Actually that is how you install a toilet. You use, strangely enough; closet (as in water closet, an old time name for a toilet) shims. They are made specifically for exactly what you describe. The toilet very often does set on the pipe and not reach the floor. You shim the fixture to prevent it from rocking.