Routing for F5

Based in your scenario, the firewall should have an interface in each network. So, no need for routes in the firewall.

An access from the Internet, should go back via the Firewall because the auto last hop. However most network engineers don't know this functionality, so it may cause confusion during the troubleshooting. Also, when traffic starts from the F5 to the Internet or other part of the network, you will have to have a default gateway or static route using one of the interfaces.

I would suggest the use of route domain for that. That is basically VRF in F5 world. That would allow you to have multiple default gateways, also provide another level of segregation between the environments.