The core stays the same, they are only adding static types. I am certain they will make sure nothing meaningful will change in the outputted JavaScript, except for potential bug fixes uncovered by the types!
Your apps should not be affected at all.
Your apps should not be affected at all.
The parent says something different and if it were just about adding types then you need just to add a file to DefinitelyTyped which I guess happened already.
We're not even "rewriting everything in Typescript at once". We're slowly converting files over one by one. No public APIs are changed. Furthermore, we have an extensive test suite of end-to-end tests for both development and production behavior.