I didn't look at all the screenshots, but to see if this is really a NAT loopback problem, try accessing http://[your.public.IP]/pokemondpds/worldexchange/result.asp?pid=0 from your web browser while SendPKM is running on your computer, and see if something happens.
If you want to know what GTS distribution looks like from outside your network, you can use something like a webproxy, e.g. http://www.myphproxy.com/, and go to http://[your.public.IP]/pokemondpds/worldexchange/result.asp?pid=0.
For the DNS though, you'll have to ask someone else to test it for you.
If everything is properly forwarded, there should be no problem.