Can we sue for sewage damage to our belongings and cost of insurance premium hike because of claim?

Sounds like a great case to sue your landlord. I've sued for such often, so consult a tenant lawyer to see what your options are.

How long do I have as a tenant to demand a full refund of my security deposit.

After you move out, the landlord has 21 days to refund or give written estimate of costs.

Am I able to vacate a house in which I am a tenant with no lease agreement due to unresolved mold issues?

Yes, if a home is uninhabitable you can cancel the lease. I've sued landlords for mold like what you describe so you should consult a tenant lawyer...

How many days do I have after receive a eviction paper file at court?

You have 5 days to answer a UD. However, from what you describe you have affirmative defenses. Consult a tenant lawyer.

Renting house with several code infractions according to city. Can I sue?

Yes, it is. I sue landlords all the time over this, especially if there are no permits. Lack of water heater is a great cause of action as well....

How long do I have to hold my ex boyfriends things at my apartment?

This isn't strictly landlord-tenant since there's no landlord involved. It's a messy situation with you as possible caretaker of his stuff. Legally...

Yes, you can, or they owe you a refund if you've already paid. Not having a hot water heater can amount to uninhabitable conditions, especially in...

Landlord Responsibility?

Do you mean home repair? If yes, then the landlord can't collect rent, but does not have to relocate you or your stuff per se. If there's liability...

How can I evict a tenant?

Get a lawyer to do it. You're his landlord as a sublet.

How do I file an 'extension' to vacate premises for my business when I am not living in the country?

You would need a lawyer to file an ex parte motion. Only a lawyer can do it if you can't do it yourself. No one else is allowed to represent you...