standby stays active

I was asked to setup a virtual server with 2 pool members in active standby. This can easily be accomplished by configuring priority group. However, in a failover scenario, they don't want the standby member to fail back once the primary comes back up. Priority group can't help in this case. Is there a way to accomplish this?

Not without some work - the LTM is not designed to implement pool member switching, which is what you are describing.

You could set the pool members to require manual intervention before marking the primary up. However, this may cause issues if both members are marked down.

You could also investigate using iCall automation - triggering an event when a pool member goes down in the pool, and modifying the priority of the members.

Another requirement is that the application listens to 7 different TCP ports and they wanted the F5 to track 2 specific ports so that if one of those 2 ports fails, take that member down despite the rest of ports are all good. How can I do this?

Set up your node with tcp monitors on the specific ports, and set the Availability Requirement to "All"