You can use packet filters to restrict access based on source and destination hosts/subnets and/or ports through LTM. ASM is a layer 7 firewall which can validate application traffic for HTTP(S), FTP and SMTP.
As for routing, assuming you have self IP addresses defined on the VLAN that the pool members are on, I think LTM uses that VLAN to ARP for the pool member by IP address to send traffic to. Routing isn't used in that case. If you don't have a self IP on the same subnet as the pool members, then the routing table would be used.
To send responses back to the original client, LTM uses a feature called auto lasthop to record the source MAC address and interface to send the response back to. Again, the routing table is not used for this.
Aaron