Actually. I would more recommend using lighttpd than Apache or uhttpd. I don't know why but I feel that lighttpd is more faster, stable and uses less resources that anything.

Well, As per what I think I think it is not possible to run the windows application in Omega2. You need to have WIne and make too much of adjusments to make it work which will not work because the Omega2 has little resources for these kind of work.

You need to get an API integrated with a python or anyother language, put it in a cron job and make it run under a cron job so that the script executes and changes the IP in No-IP.

All these are just right away from my brain making imaginary calculations. The No-IP may not have an API. If that is the case, then I am sorry - I can't do anything more.

If whatever I said is correct, then give me a thumbs-up. Or, if it is wrong, then do ping me back and I will correct it accordingly to it.