What is the bigip address in the above config? Is it the self IP of the internal VLAN, 1.1.1.1, and will this also be the default gwy of all servers sitting on the internal vlan?yes
When the external incoming traffic frome hits the virtual server on, 3.3.3.3:80, while trying to load balance the incoming traffic to the servers in the pool, bigip would change the source ip of the incoming packet to that of its own IP you can configure to translate source address (snat) or not. if you do not translate source address, you have to make sure return traffic will send to bigip e.g. pool member's default gateway is bigip.
and change the destn ip from VIP,3.3.3.3, to one of the servers in the pool, based on the load balancing method, .....Right? yes
bigip would take of routing between the VIP and the internal VLAN range, right?if it is not connected subnet, route entry is required (definitely, you are able to configure route in bigip).