VIP type of Forwarding (IP) with fast layer 4 profile

You can configure a fastl4 profile attached to the virtual server and enable loose initiation and loose close and make the virtual server stateless (purely a router). Keep in mind the vlans where you enable the virtual server, there is where you are enabling routing.

I don't understand your second question. If you want to make a virtual service available you don't need a forward virtual server for that, it is easier if you just configure the virtual server to listen in the vlan where the traffic reach your big-ip.