use port 443 for VIP and pool members

Inline again.

3.) That may be a tell-tale indication of the problem. I'd start troubleshooting this health monitor. 
>> i can see the nodes become red or green in short seconds..not sure if this cause the issue. any correct param tcpdump can use to collect? 

Generally speaking, there's a few places to look. The LTM log (/var/log/ltm) should report health monitor outages. You can also tcpdump on the internal network of the BIG-IP where the servers are and simply watch the monitor traffic. It may be that the server isn't responding exactly as you'd expect it, or that the monitor is misconfigured.

4.) A failover event will get logged, and you'll see an active unit go to standby in the GUI (and a stanby unit go active). Do you not see these things when you disconnect the active unit? It could be that what you think is the standby unit is actually the active unit, or perhaps that your HA is misconfigured and both devices are active. 
>> No, I not see the active device become standby when unplug the lan cable for e.g. lan cable connected to interface 1.3 and 1.4 in f5 active unit. could this due to the web server teaming are not working properly which connecting directly to both f5 units?

HA status has nothing to do with how the web servers are connected to the BIG-IPs. It has to do with how the BIG-IPs are connected to each other and how HA is configured. If you don't see a state change when you do something that should force a failover, then there's something wrong with the HA configuration, or perhaps that you're HA config isn't listening for the event that you think should be causing a failover.