Pihole wrong client IP & DHCP not detected

Try run nmap from a client PC.
Running nmap from the same host thats serving DHCP is going to fail.

Sounds like rebind protection:

Try enable DHCP on Pi-hole,
connect a client PC, with network settings set to auto, directly to Pi-hole without router in between and
run below one on the client to check if resolves:

nslookup pi.hole