My Virtual IP doesn't work?
Hi Node is showing unknown because you haven't configured any node specific health monitor while configuring the node. Now your virtual server is showing available it means the backend pool is available and the pool member is listening as well as reachable on the required web-service port. So with this configuration, you should be good.
Now coming to the issue that web app not accessible from client system, i would recommend you to check the traffic hits on the virtual server as well as pool under statistics. This will clarify that the request is reaching the F5 virtual server and hitting the correct pool members.
If traffic is reaching properly, then check the SNAT (Source Address Translation) settings on the virtual server. If backend web-server don't have F5 as its default gateway, you need to enable SNAT (Source Address Translation) settings on the virtual server and you can set it to Auto-map. Basically this will avoid the asymmetric routing issues.
Please check these points and confirm if it works!