If you aren’t connecting to any other networks, you don’t need to add routes to the layer 3 switch. Think of it as a router. If you configure an IP for each VLAN, the router will automatically know about that subnet and the VLAN associated with it. On the other hand, if you need to reach other networks not directly connected to the router, you will need to notify the router in some way. This can be with a static route statement or by using dynamic routing like RIP or OSPF.
As for the trunking, in the non-cisco world, this is referred to as VLAN tagging. You will have to configure all of the VLANS you want to pass through a switch, even if no user ports will be mapped to that VLAN.
For the port connecting the switches, one VLAN can be untagged. This is called the native VLAN in cisco language. All of the other VLANS running through the port have to be tagged. If you do this, you can run all of the VLANs to every switch so they can be brought out wherever they are needed.
Once you have configured VLANs on an HP switch, the way to map a user port to a VLAN is to set that port to use just that VLAN untagged.
The VLAN section under the switch configuration menu is fairly straightforward. Once you have created the VLANs on the switch, the VLAN port assignment section is obvious.
Typically, a router/L3 Switch will be able to route VLAN traffic through known and/or connected routes as long as IP routing is enabled. And, from a layer 2 device to a separate L3 device, trunks are usually the best way to inter-connect all VLANs