Is anybody familiar enough with New York City 1999 National Electric
Code to be able to answer the following two questions about electric
safety:

1. Is a bathroom considered a damp location requiring it to conform to
Article 410-4 for fixtures in damp locations and 410-57(a)for
receptacles in damp locations? It seems to me that the definition of a
damp location is one constantly subject to dampness as opposed to a
bathroom which is only damp when using the bath or shower.

2.Is a 115V 15A Duplex Receptacle allowed on a 20 A circuit if it is
the only receptacle on the circuit?

This is not specific to New York City law, but it may be useful:

"Damp Location
ULC listing for fixtures used in a moist unexposed area, such as a
bathroom or porch area."

http://www.norburnlighting.com/id16.htm

I think you need to contact the NYC Department Of Buildings at
WWW.NYV.gov or if you live in NYC call 311 they will direct your call
for Free.

http://www.nyc.gov/html/dob/html/elcode.html

This should Help yuu  out.