Is it possible to create a custom keyboard and upload it to the App store?
Yes, lots of people have done this, you can find many custom language keyboards in the app store.  You should make sure there is not one there already by searching the store for the language you are talking about.

Have a look at the Keyman app.  It already has lots of keyboards and I think offers ways to create new ones. 

Keyman 

For developer info see iOS Custom Keyboard