The openSPOT1/2/3's bootloader only writes the differences to it's flash memory, so nothing will be written to the memory if you try to flash the same firmware file again. CRC checks are also performed to ensure that the written firmware matches. If your openSPOT2 boots then it already has a correct firmware.
Please see my answer on the duplicate call log entries here:
https://forum.sharkrf.com/viewtopic.php?f=9&t=3935
(the "send no in-band data" has nothing to do with this).
You don't need to power cycle the openSPOT2 when the web browser goes to sleep. Just reload the page, or re-open it with sharkrf.link.
We don't know why the OS2 can't communicate with your DHCP server. Use the OS2 with a static IP address if that works for you.