How do I get a lawyer to speed up the divorce process just a little?

You should speak to your lawyer and expect the case to last up to a year in real time.

If I pay for a background check on myself is it my property?

sure you can and of course you have a copy but if it was required they will keep in their records as well.

Is this legal

Sure seems shady consult local landlord tenant attorney for review.

File subpoena in Court have your process server serve.

Modify house arrest

Hope you can get it modified what does your lawyer and p.o. say?

Can a child be taken out of the home because the mother admitted prior dug use but has passed drug test now?

Yes absolutely, best to hire a family/cps lawyer asap.

Can I use the washer/dryer in my building?

Sure you have a claim and you have answered your own question read your post back to yourself.

How do I request criminal records?

Hire private investigator or company to run background check.

How can I get time with my son?

Consult local family lawyer to assess and advise.

Can a custodial parent request reimbursement for 8 years of medical expenses that they never informed the other parent of?

A parent can request whatever they want. Your divorce decree court order controls, no clue as none of us have your decree nor know what is ordered.