I was wondering if there was an app for Android with which I could access Ask Ubuntu? And if there isn't, and I wanted to write one, is there an API I could use? Where can I find more information on this?
You might want to look at this list and find one you like. If you don't like any of them, you can find out about the API at http://api.stackexchange.com/ . Although many apps mention Stack Overflow by name, the API is the same for each Stack Exchange site, so almost every app will let you choose which site you're accessing.
While they all have different features, you'll notice that none of them have the facility to post new questions and answers. This is a feature deliberately left out of the API to keep people using the website and ensure the site doesn't fill up with autogenerated posts or broken formatting.