> One F5 VE VM has four VMNICS, 2 for Management (VMNIC0 Active and VMNIC1 as standby) and 2 Production (VMNIC 2 primary and VMNIC3 as Standby).
First - you can only assign one VNIC to Management - it's a single interface. On a VE - it's the first VNIC.
> and 2 Production (VMNIC 2 primary and VMNIC3 as Standby).
Again, this isn't how it works - the VNICs are connected to the virtual network infrastructure as Interfaces 1.1 and 1.2. You may be able to define the two links as a trunk.
> Do I have to define individual Internal and External Interface for each Pool Members?
Are you talking about pool members (i.e destination servers that deliver content) or virtual servers - listeners on the BigIP that forward traffic to the pool members.
> AS the Internal VLAN can't have a default gateway on F5 since they are connected with the Cisco switch, what would be the Internal Interface setup look like? Will it be Just a tagged Interface with VLAN 100 and No "non-floating and floating Self-IP"?
Every VLAN (tagged or untagged) has to have both non-floating and floating self-ip addresses to accept or send traffic.
If your internal servers cannot have their default gateway set to be the BigIP, then you will need to SNAT the traffic so that the return traffic from the pool members goes back to the BigIP.
> My ultimate goal is to setup the F5 VE HA pair to act like an One ARM but having External and Internal VLAN are in different sub-netwrok. What would be my setup in this case?
As I said before, a one-arm setup only has one vlan. You do not appear to be doing this.