How are you connecting the Kentico API externally? Are you just including the libraries or something, like in an MVC style setup?
In order to connect a seperate external site to Kentico, you need to follow these steps:
Unless your external system is simply using Kentico's REST services, which then you'll want to look at the article on the REST services.
For #2, importing / exporting users, do you do a System -> Macros -> Resign macros and also a clear cache/Restart application after you do the import? sometimes this resolves these weird bugs when importing from another location, otherwise i can't give much guidance on it, I've never imported user from another Kentico instance.