We do have a fully-featured API, in fact our mobile apps are built on top of the same API as the website. At the present it's not documented, this will be happening as fast as we can work on it. We're a small 3 person company so things like documentation take a back seat sometimes. If you're handy with a browser console you should be able to poke around, pm me if you want an API key :-)
The site itself is free, and you can print material that you create. We only charge for premium content which is material that we've specifically created for exams and is guaranteed to be high quality and accurate.
We allow for imports from top flashcard programs including Anki, however Anki files tend to be large so for the time being there is a 10MB (I think) cap on the size of an Anki deck you can upload. I can do it manually for larger decks if you pm me. Export is something we don't support at the present, but will probably get built at some point in the future.
Happy to help you design something for your coursework, we are actively looking to build an educator service allowing you to share course materials with students. Stay tuned for updates on this in the near future.
You do really address the issues that prevent me from using Anki, and I'd be happy to pay for it once you do have that API.