Replace babel by typescript

[lukasjuhrich]

@sebschrader mentioned that with a working typescript setup, one may think about using typescript to compile all of our javascript, and not only the (future) typescript files. In that regard, it would not serve any purpose to compile and then transpile things again; typescript has its own backward-compatability-capabilities.

[lukasjuhrich]

An argument for babel would be that we might utilize it to transpile .jsx to vanilla JS. But perhaps this works with typescript as well.