Can we downgrade oracle database form 12cR2 to 12cR1

To me it looks like you did not start the listener but it is started. Your problem seems to be the tcp connection and not the ipc. So the listener is running, you can not reach it using tcp. Test this using telnet gaurav 1521

If the telnet does not give a connection, a firewall is blocking you. Stop/edit the firewall.

Unless your development or testing team already has a set of regression test cases, you are out of luck. The possible things to test are astronomical. Now, as others have pointed out, there are some things to look out for, like more restrictive privileges, and reviewing the "What's New" for both 11g and 12c.

One big example from the past that burnt a lot of people (including me) was upgrading from 9i to 10g; where developers relied on a "group by" clause in a select would always return the results sorted by the group by columns in 9i, but not always in 10g. Not a bug; the SQL standard for group by says nothing about ordering of results; so a lot of code broke. But again, only way to flush out those types of things are good regression test cases.

Now, after all that, I have not seen or heard about any 10g to 12c surprises, but there are a lot of wonderful new features that should be used when moving to 12c.