I have attached my router settings where there are few Settings which i am not sure if it has to be enabled. Kindly help me. At times the PI Hole doesn't seem to resolve even google.com. Just wanted to rule out the possibilities
I am concerned about
Enable Primary DHCP server
Enable DHCP Relay
Enable Option 125
Also when will by Secondary DNS Server be used ? When my pihole is down?
You have a "secondary" DNS server assigned, and this is likely allowing some of the DNS traffic to go to a DNS server other than Pi-hole. When clients have multiple DNS servers, they are free to use whichever they choose.
Read the manual for your router for descriptions of the other three options you noted.