Whom does an agent listing an apartment represent?

not you, the seller or themselves for a cut.

From a legal perspective? To whom do they owe fiduciary duties? If they screw you, can you sue them? If they tell you things and they're an agent of the renter, can you later bring these up in court if there's a dispute over the elase?

Does their license impose any requirements on them at all to be truthful (realizing many may not be anyway)?

I believe technically they would be agents of the management company. However that does not mean that they are not obligated to be truthful with the renter and treat them fairly in every way. You could have had a shady agaent, or it is possible they were truthful. Leases in nyc often have provisions that in "real life" are never enforced, and they may have been simply letting you know that---or not. Yes they can be sued for misrepresentation regardles of who they represent.

An agent represents and owes a fiduciary responsibilty to the party that is paying them- in this case the management of the building or the owner of the apartment, unless the tenant will be paying and then they are a buyer's broker. Ethics requires the agent to treat all parties fairly and honestly however, it would be naive to believe that everyone operates ethically. The NYC Board of Realtors would oversee any complaint of breach of duty or lack of ethical behavior.

I believe it's still the bizarre norm in NYC that the owner/manager doesn't pay a rental broker -- the tenant does, and handsomely so.

This despite the fact that rental brokers are just performing outsourced functions of management offices.

Your experience is one of the happier ones described about rental brokers. There really needs to be legislation making it illegal for a broker to be paid by the tenant, just as it's illegal for employment agencies to be paid by the employees.