How can I get my former employer to provide me with an accurate pay stub that reflects what will be claimed for this tax year

Sounds like you have may also have claims for minimum wage and likely a few other claims. Contact an employment attorney.

What are the law requirement for a living HHA? To be more pacific the sleeping arrangement?

You may have rights to recover wages. Call an employment attorney for a consultation.

You're most likely entitled to atleast overtime pay. Contact an attorney asap.

Can I do anything to get the overtime I should have been paid?

You are likely entitled to overtime pay, depending on your duties. Many employment attorneys give free consultations, you should contact one asap.

Should my husband go to the Dept. of Labor?

Contact an employment attorney. Your husband is likely entitled to minimum wage, expenses he pays out of pocket such as gas for the car, and likely...

1) Is a salaried manager entitled to a cut of servers gratuity? 2) Is an hourly manager entitled to a cut of servers gratuities?

You should contact an attorney a.s.a.p.

Is it legal for my employer to take tips from online orders?

This most likely violates New York Labor Law and possibly Federal Law depending on your hourly rate of pay. Contact an employment lawyer asap.

Depends on a few factors. Contact an employment lawyer.

Is it illegal for a salary manager to take a portion of the tips made from a dinner party in a restaurant?

Yes it is illegal for a manager to take a part of the tips. See an employment attorney asap.

Can I file a lawsuit against my past employer for unpaid overtime during my employment if I have time sheets to prove my hours?

You can probably sue your employer for the unpaid overtime. You should contact an employment attorney.