Can we run OSPFv2 on few interfaces and OSPFv3 on few interfaces within the same system? Can we run both OSPF v2 and v3 as different processes?
Sure, this is possible, depending on the router model and software. OSPFv2 is for IPv4 only and OSPFv3 for both IPv4 and IPv6. There are however differences in the implementation of both protocols (as these are two completely independent protocols), depending on the vendor and sometimes even on the model.
Consider Cisco for example: In regular IOS and IOS-XE, you can run both protocols at the same time, even for IPv4. Note however, when running both OSPFv2 and OSPFv3 for IPv4, routes learned via OSPFv2 will always take precedence, ignoring "normal" OSPF route selection rules, which are only evaluated within a process.
On IOS-XR, for example, OSPFv3 is not even supported for AF IPv4, only for IPv6.