Pihole receives no requests - home has no connection when pihole is set as dns

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How did you set the IP? Is it the upstream DNS of the router itself?
Because your router advertises itself und two public DNS servers via DHCP to its clients

   * Received 340 bytes from eth0:192.168.1.1
     Offered IP address: 192.168.1.10
     Server IP address: N/A
     Relay-agent IP address: N/A
     BOOTP server: (empty)
     BOOTP file: (empty)
     DHCP options:
      Message type: DHCPOFFER (2)
      server-identifier: 192.168.1.1
         lease-time: 86400 ( 1d )
      netmask: 255.255.255.0
         router: 192.168.1.1
      dns-server: 192.168.1.1
      dns-server: 1.1.1.1
      dns-server: 8.8.8.8
      renewal-time: 43200 ( 12h )
      rebinding-time: 75600 ( 21h )

The clients will then choose one of those DNS servers as they like to answer their DNS requests.

Set PI-hole as the only DNS server distributed via DHCP (and dis/reconnect the clients from the network to pick-up the new settings).