For static IP address, it doesn't need to get the IP address. So just need to wait for the backup WAN up. It should take less time than ddynamic IP.

You can try to set Ping as 8.8.8.8, and DNS lookup as 0.0.0.0. It means that only use Ping to detect the network status. If still need to wait a long time, maybe related to how often the router will...

If your deivces get IP address from wireless router, then you can only check their IP on wireless router. Load Balancer will only show the IP of wireless router's WAN. If your wireless router support...

It seems that T1600G-52TS V3 supports port mirror and it can mirror the packets that pass CPU. Maybe you can use port mirror function and choose the source as CPU, then check what packets pass CPU.

Genrally "G" means gigabit ethernet and "P" means supporting PoE. LS108G should be a different product serial from TL-SG108. It seems that TL-SG108 support IGMP snooping but LS108G doesn't support it.

I cannot think out other method. Maybe you can try to re-install your firmware. What's your hardware version and firmware version? But it may be a little complicated to upgrade through CLI command....