No, only one trading account can be opened with one broker. However, beneficial owners can open multiple Demat accounts with as many DPs or brokers as they want.
Stockbroker charges vary widely and depend on various factors such as the type of broker (full-service or discount), services offered, account type and the volume of trading. Some stockbrokers charge flat fees per trade/order others charge a percentage of the transaction value. Some even charge annual maintenance charges or a combination of these.