1. Modbus is a open protocol that was designed by Modicon. It is accepted as a defacto standard. It was designned for transmitting non-critical non-deterministic data bewteen PLC's.
Profibus is a propriety protocol, which is "owned" by Profibus International organisation. It is an accepted industry standard (and used almost exclusively by Siemens industrial products). It is designed for the transmission of real time, mission critical I/O data.

2. This also depends on the transmission medium as well as the protovol. Modbus supports up to 249 slaves and 1 master. Profibus supports up to 124 nodes, which can be masters or slaves. The transmission medium further restricts this. Modbus can be used on RS232, RS422 and RS485. The maximum limit for RS232 and RS422 is 1 master and 1 slave. The maximum limit for RS485 is one master and 31 slaves. Profibus is based on RS485, and thus can only support a maximum of 32 nodes. The RS485 limit can be expanded in 32 node increments by use of repeaters up to the maximum protocol limit (this applies to Modbus and Profibus).

3. With modbus one and only one master is permitted per network. For profibus you have 32 nodes (without repeaters) or up to 124 (with repeaters). I believe that any / all of which can be masters. I may be wrong, if so, I'm sure someone will correct me.

4. I do not know what you mean by define the standard. The Modbus is an open protocol and information about the protocol is freely available at  www.modbus.org  For Profibus, the standard is controlled by Proibus International orgaisation. The details of the protocol are not freely available. You can only get the protocol specification if you become a member of the Profibus International organisation, which is subject to an annual fee.