Can we use both RSTP and MSTP spanning tree protocols in same network

RSTP and MSTP were developed from the ground up to make them work together. We can see MST as being a extension over RSTP. The MST BPDU is in fact and RSTP BPDU + some few additional things required to support several instance. So basically, from the perspective of an MST bridge, an RSTP peer looks like a different MST bridge in a different region. We don't find any issue running RSTP and MST both except of course that you will only be able to run a single instance (instance 0, the CIST) at the boundary between RSTP/MST. Hence hop count MST uses is only within a region. Between regions, MST uses the message age, just like RSTP.

Cisco will not support a real RSTP as defined in the IEEE. We only have Rapid-PVST, which is a proprietary version running one instance of RSTP per VLAN. The trick is that we don't need to support IEEE RSTP because MST is a superset of RSTP. Running MST with no region configuraiton is basically equivalent to running RSTP

Yes, MSTP and RSTP interoperate. Practically, RSTP works like unconfigured MSTP with a single instance and region. RSTP peers are treated like MSTP peers in the common spanning tree (CST).