CAC authentication and http headers

For this case,

1. Separate new pool for the new server.
2. Yes you can use LTM policy or iRULE to send traffic to the desired pool based on the URL host; uri etc.

NOTE- Adding a new pool member in existing pool will create problem. As for any host request, the request will be forwarded to all the active pool members in the pool. So with this, client will get unexpected response pages.

Hope it helps!

I do not see any conflict / issue with such configuration if the LTM policy or iRules & SSL configuration is done properly. Now As vServer is configured using iApp template, you will need to modify changes restrictions on the iApp template in order to make changes on the vServer.

But you will also need to consider other side story. As both ADFS & the new URL will be on common vServer, whatever changes you will make on the VS, all the changes will be applicable to both applications. Personally I would prefer to have dedicated vServer for services like ADFS. Otherwise having normal URLs on the common vServer works fine.

Hope it helps!