Always advisable to register agreement. it should be duly stamped. If the rental agreement period is beyond 12 months, it would mandatory to register the same before the sub-registrar office.
Yes, it is valid to have a 3rd party witness in a rental agreement to avoid any kind of disputes in the future. It is always advisable to have a 3rd party witness in order to provide a layer of security for both the landlord and the tenant.