I believe you've done too much and maybe created a DNS loop somewhere causing heavy load on Pi-hole resulting in those timeouts.
Only enter the Pi-hole IP address on the Fritzbox DHCP settings page as a single DNS server and no others!
Default the rest of the router settings.
And I believe Fritzbox needs some more tinkering with its settings (maybe rebind protection).
Search discourse here for Fritzbox or wait for another Fritzbox user that knows.
I believe there are plenty.