OctoPrint web interface freezes, SSH terminals freeze, printer is happily printing away

Have to try that still.

Difficult to test it because it happens so randomly.

We have a similar thread going on here - OctoPi losing network connection mid-print

No answers to the problem yet, but the info there may be helpful in tracking down the source of the issue.

So right now OctoPi again stopped responding during print. The print is still going on but the OctoPi is unreachable.

I assigned a static IP address and started it in safe mode. Still no luck though...

If your problem is network connectivity (and this sounds 100% like it is) then safe mode won't help you. Since you assigned a static IP it isn't DHCP leases either. Next step is testing with an ethernet cable. If that works, something's making your Pi get kicked off the network.

Want to mention second bug (not first time I've seen that problem, had to power cycle).

There are two separate bugs:

[#1] wlan0 would be down, egar had a great script solution (restart network service if it's down)
[#2] wlan0 would be permanent down, not even egar's script would fix it (see screenshot)

Having the same problem. Pings will drop off and usually don't come back until a reboot on the pi.