Rent stabilization covers a large share of the older housing stock and governs both the increase and the renewal right. Whether a specific unit is stabilized is a question with a documented answer — ask for the rent history rather than accepting a listing's word.
The FARE Act moved the broker fee to the party who hired the broker, ending the long-standing practice of charging a tenant for the landlord's agent. Budget the first month and the one-month security, and query anything beyond that.
Short-term letting under thirty days without the permanent occupant present is unlawful in most of the housing stock and is enforced through a registration regime. It is not a grey area.