I would like to be able to ping my public IP address, I registered on no-ip.com and I set up my no-ip account in the openwrt interface on TPLINK MR 3020 router.
So I'm supposed to have a public ip fixed, but I can not pinger from my windows console?
Your ISP has to have set up "hairpin routing" to allow a meaningful test of pinging your own public IP from the same connection.
The usual way to access your public server from inside the LAN is to add an alias entry to the local DNS, so when someone on the LAN goes to public.myname.com, it gives them the internal LAN IP instead.
Testing incoming connections is best done from outside:
Separate ISP, e.g. tether a mobile phone.
Port scan site.
VPN service, tunnel out via VPN then connect back to your public IP.
Shouldn't it be his own IP address on the WAN interface of his router?
Although, it should be true in case of ISP NAT, but in that case the OP has no public IP and setting up DDNS is pointless.
Depends on the type of ISP-NAT. There are some (although very rare) cases where ISPs implemented 1:1-NAT (don't ask me why they would do that, but they do exist). In that case, the only pitfall is that the router won't be able to see its public IP, so DDNS service needs to use the IP that the request is received from.