How many transmitting and receiving antenne are there on a mobile phone tower ?

Apart from communicating with mobile phones, the towers have to communicate with the control and switching centres.

Normally three transceivers cover 120 degree each. This is meant exclusively for mobile traffic and has limited range (cell)

Mobile towers are interconnected via optical fibre cables.

For monitoring of a group of towers and their data, additional wireless channels are used which communicates with the switching or control centres regarding their status and various parameters like power condition, site traffic, equipment status etc. This complements and also serves as back up for Optical fibre cables.

Hence you may see additional antennas apart from the three or four regular ones.

If the site serves a larger than normal distance, there will be additional receive antennas to provide for diversity. Do you really mean mobile radiophone service or cellular service as they employ very different technology.

It depends, some towers arent just for one provider, as they tend to share towers sometimes.