Can you please confirm if "Cisco Catalyst 3560G-24TS" is a layer 3 switch or layer 2 switch.
After upgrading the IOS to advanced IP services i still could not see any options in Cisco DM to configure IPs on each port or IP on each VLAN.
Yes it does intervlan routing , with ip base its static and RIP and eigrp stub i believe . With enterprise it will support all major routing protocols bgp,ospf,eigrp etc... Wish I could help you with the gui but not too many people use it in this forum . Most of us are CLI geeks :-)