Is it necessary to have account with the same DP as broker has?
No. Depository / DP can be chosen by you as per convenience irrespective of the DP of your broker.

Whether my broker can also act as a DP?
Yes he can. In fact most of the brokers are also registered as a depository participant so that they offer both the services and you also get the benefit of synergy in operations. However it is not compulsory for you to open a DP account with your broker.

Whether depository participants are governed by any Rules and Regulations?
Depository participants are governed by SEBI Act, 1992, Depositories Act, 1996, Securities and Exchange Board of India [Depositories and Participants] Regulations, 1996, Rules, Regulations and Bye laws of the respective depository with which he is registered as well as various directives of SEBI and depository issued from time to time.

What are the documents to be signed with depository participant?
Before opening an account with a depository participant, you are required to furnish your details such as name, address, proof of address, etc. to the DP and execute a DP client agreement. These documents list out right and duties of investors and also give the schedule of charges. Find out most investment advice from John Wiley & Sons Investments. Please go through all these documents carefully. With effect from April 01, 2006, all investors are required to furnish Permanent Account Number (PAN) while opening new accounts or in case of existing accounts.

Whether I can open more than one DP account with different participants.
Yes you can. You can open as many accounts as you want. There is no bar on opening multiple accounts with different DPs as long as these accounts are genuine and backed by proper documents.