Best method to tile over concrete block with drywall glued over it?
There are not many options to resolve this properly. So I will address your questions first.


  1) Do we need to install some kind of vapor barrier in this scenario?


The current best practice is to place waterproofing over the backer board and just under the tile. (ie Kerdi waterproofing)


  2) Can we use insulation board between fur strips and if so, foil facing tile or away from tile?


The answer is no and for the same reason no vapor barrier is to be used behind the backer board. The wall cavity should be able to breath and allow any moisture to evaporate.

Updated: Based on finding out it is a basement

So my answer to you is: 
As mentioned by Ed - Spray with water to soften the drywall and it should easily come off to the paper.

Inspect and choose best method of removing glue: if it was glued unevenly.
Maybe snap lines or draw lines as a layout for furring strips. (no need to do more work than needed)

Fasten furring strips, use backer board, seal (recommended) with (ie. Kerdi waterproofing) and tile over that.