building at 737 Park Avenue

No, not since Macklowe bought it in 2011 to convert to condo. There'll be rentals once some of them have closed.

I think some old rental listings from 2009-2010 were just cleaned up in the SE database. That history creates the illusion of an active rental market.

Can the ugly beams be removed from the ceilings.

They are typically structural and can not be removed. You can drop ceiling to cover them. But beams are in important prewar feature and many consider them desirable.

Yes, I think the beams are, in fact, on of the most attractive features of prewar buildings. Sometimes they are asymmetrical, but that can be a relatively easy fix. I added to the beams in my prewar coop. If you want to cover them up, why not buy into a boring white brick building with 8 foot straight ceilings?