Carrier frequency and transmit power of a commercial aircraft
At what (central) frequency does an aircraft communicate with a
  control tower?


This is different for every tower, although due to the limited discrete frequencies around the globe they are repeated, generally far enough apart its not an issue. Specific frequencies can be found for US airports on either charts or in the AFD. 


  Is the communication over one frequency only?


Generally every tower only has a single frequency, there are some airports or enough traffic to warrant multiple frequencies. They are often segmented by approach direction or runway. 


  How much is the transmit power of the antenna? Is it per hertz?


Transmit power may vary based on airport but should be constant across the frequencies. 


  Also please correct me if I’m wrong: From my readings,
  aircraft-airport communications is analog only, correct?


Not analog only, digital comms are used. For the airport environment there are systems such as CPDLC for delivery clearances and D-ATIS for digital airport information.