Is their a place in the mall to replace a watch battery

Yes

Yes there is

Time Square does this service for a reasonable fee, usually only the price of the battery. They are located on the first floor, inside the main mall entrance by crate and barrel, just pass the escalators

What's the name of the place?

Yes, just check in at the information desk to find out where the location is.

Yes it's on first floor

Depends on the watch, but yes to many watch batteries

I am sure one of the jewelry store's can do it