I have setup with FCI+AG solution but with independent disks
The FCI doesn't work without shared storage, so I'm going to assume you meant to say, "I have setup with FCI+AG solution but with asymmetric storage".
There is no listener, and the applications are connecting to the FCI. Is this setup even reasonable to use?
The no listener part is going to severely impact transparent DR, but this setup is possible although not wise. Is it reasonable to use? Sure, just not in its current form - which is mostly due to the connecting through the FCI name and not a listener. Everything else is fine.
The only option I see here is manual fail over.
The AG will be manual failover, yes. However, there is a huge asterisk here which is that whenever AGs are used in conjunction with FCIs, there is no automatic failover at the AG level. The automatic failover will happen at the FCI level and the only failover method for AGs would be manual.
If I need to make any changes, what can be done?
What kind of changes are you looking to make? Personally, at the minimum I'd setup a listener and have the applications use that. Otherwise it's going to be an even more painful AG failover experience.
Can I add a listener to the AG because both the nodes are in sync?
Adding a listener does not require the AGs to be set to a specific availability mode. AGs can have 0 or more listeners (only one available to be added via the GUI) and be in any availability mode.
From a storage perspective was this supposed to have a Shared SAN instead of independent disks?
The FCIs are using shared storage... it's a requirement. It's not a requirement to have shared storage for AGs.
