Should I seek rent abatement from my landlord when we have no cooking gas, even though he provided an electric stove?

You should start an HP action and sue the landlord in Small Claims Court for an abatement.

Is there a legal basis for moving out under a month to month lease from a basement, if the air is making me sick?

Call 311 and have a violation posted. Then you can sue in Small Claims Court for return of your security deposit.

Is there a way to force building management to fix radiator noise because of a medical condition?

Under applicable Federal, State and City law, your landlord is required to fix the situation.

May I counter sue for a false/made up back rent amount?

With some minor exceptions, if your apartment is illegal you are not required to pay rent. However, before withholding rent you should meet with an...

Preferential?

You are entitled to your preferential rent even if its only $1.00. i do not understand the rest of your question.

If the apartment is illegal you most probably do not have to pay rent. However, you must retain an attorney before you begin withholding rent.

What are the laws if any on living in a dirty filthy house with flies flying around and can i take money off the rent

Call 311 and file a complaint with HPD.

You appear to be entitled to a rent abatement and damages. However, you should never withhold rent without first obtaining an attorney.

You do not have to voluntarily vacate. Your landlord is required to bring a Holdover Eviction action against you. When in court you can request...

Received 60 day notice for lease on apartment, can we stay longer if we can't find a decent place in time? Do we still pay rent?

You cannot legally be "kicked out". Upon your lease expiration your landlord will have to start a Holdover Eviction action against you in Housing...