At first I was really enjoying implementing this plugin, but things just don't appear to be working out for me.
Hi 
AnD4D, I'm sorry to hear this plugin doesn't work for you while it works for nearly 100 other people who use it. I'm happy to help but it's just hard without seeing the exact process you do to build an app, so I'll be guessing a bit.
You also mentioned in the email that next to the IAP, you also have a problem with setting up the AdMob plugin. The good news is that I have made (also many of my customers) many apps with IAP and Ads implemented and it worked perfectly fine both for Android and iOS which apparently proves that all works fine if you set things up properly. Now we just need to find out what's the issue with your setup.
Implementing the Ads properly should be very clear as there is a complete video series for Ultimate Ads (AdMob) available.
Unfortunately, I haven't ordered video tutorials for Ultimate IAP yet. Tutorials made by professional tutor costs a bit so this will have to wait.
In a meantime could you tell me few things:
1. Does your issue appear both on iOS and Android?
2. Have you tested on any other smartphone?
3. How did you refund the product (process and platform)?
4. Was it a Google test product or a regular product and if so what type of product was it?
5. Do you have your Google Wallet setup completed?
Products are managed by Google Play and it's Google's database that tells whether the product is purchased or not for the particular amount. So if the "has product" returns true after refunding or the purchase button instantly triggers successful purchase, then it means that the product has not been refunded in the Google's database. The plugin itself does not have a refund action and it does not store any refund nor purchase related data. It's just the API for Google services.