The TypeScript team are deliberately reserving judgement on the official coding standards because they want to see how people use the language in real life. Anecdotally, people seem to be following the JavaScript naming conventions, i.e. ModuleName, ClassName, functionName.
You can write your unit tests in TypeScript (tsUnit) or JavaScript (Jasmine, QUnit et al).
How you integrate it with CI depends a little on the framework and on the CI platform. I have integrated tsUnit tests with Visual Studio and TFS using the MS Script Engine to execute the tests. If you want more details on this particular set up I am happy to share.