Why does the Internet modem goes into standby mode overnight?

I did'nt notice that, but it's probably to reduce night lighting for people sleeping in the same room as the modem

I have no internet in this state unless I reboot.

Try going to your IP address and make sure you don't have standby/sleep on

This is not normal and you should contact Fizz to have it fixed if it continues

There is no standby mode nor is there a sleep mode. This is not normal and it should be fixed. I recommend you do a factory reset and test again. Also verify your power outlet and power cable. If you're on a powerbar, plug directly into the wall.

Stand by mode?? I don't think there's a stand by mode on that