Do you have an api? Where can I learn more?

Yes. Currently, our API is capable of driving and interacting with our automated screenshot solution. With it, you can incorporate our service into your production work flow. Calling our api is as simple as:
curl --user username:password http://crossbrowsertesting.com/api/screenshots/show

You can read our post introducing the api or check out our docs.

Comments

No way to run new tests

Your documents say "When running a new test, it will be based on an existing test.". This is a serious restriction, IMO. This means that I cannot run a test using the API for a URL which has not been tested before.

Running a new test

You can specify the a url, which creates a new test, with the screenshots/<test id>/version/<version id>/run command by specifying the url parameter at the end - see http://crossbrowsertesting.com/apidocs#132. The example shown is:
http://crossbrowsertesting.com/api/screenshots/9992/version/321/run?url=..., which would use the exact configuration settings (ie list of browsers with certain resolutions) from test 9992, version 321 and would create a brand new test id # using the given url.