1 is included in at least Google interviews. 3 requires that you hire for a specific tool/language use, most programmers are able to learn new tools and languages in the time time periods that are hired for.
I'd like to do more of 2, understanding, debugging, fixing and refactoring code is, in my experience, more of the day to day work than writing entirely new code. I don't know why this is not typically part of interviewing, maybe there's some reason it doesn't work? It would be interesting to see a more comprehensive evaluation of this approach.
1) open ended design questions 2) here's some broken code, fix everything 3) probe depth of understanding of tools/language
I always feel the Algo whiteboard questions feel like a "did you take the same DS class I did" round.