No. There are no restrictions on the number of DPs you can open accounts with. Just as you can have savings or current accounts with more than one bank, you can open accounts with more than one DP.
Yes. Foreign tourists during their short visit to India can open a Non-Resident (Ordinary) Rupee (NRO) account (Current Savings) with any Authorized Dealer bank dealing in foreign exchange. Such account can be opened up to a maximum period of 6 months.