I am wondering what's involved in switching out Mountain Bike (MTB) shifters to integrated road shifters while keeping the rest of the MTB drivetrain (derailleurs, cassette, etc.) unmodified.
Note that I am not interested in bar-end/ friction style shifters as is popular on touring bikes. I'm already aware that's an option. So below, by road shifter I mean integrated shifter/brake lever like Shimano's STI or Sram's double-tap.
A similar question was asked here but the answer focused on the derailleurs and didn't say much about shifters.
I'll ask this question in three parts (feel free to only answer one):
Generally speaking, do all MTB derailleurs have some road shifter with which they would be compatible? Or if you were planning on buying a MTB with the aim of switching to road shifters, would you need to be careful about your initial choice of MTB drivetrain? I.e. can you just buy whatever bike and build you like, then find the road shifter that will work with it? Or do you need to restrict yourself to a subset of MTB derailleurs for which you can actually get compatible road shifters?
What are the criteria for finding a road shifter that will work with a particular MTB derailleur?
For a specific example, and to clarify why I'm interested in this, I want to get a fat bike but because of some wrist problems, I have trouble with flat bars but no trouble with drop bars (where I usually ride on the hoods). In the price range I'm looking in, I'm seeing that a lot of fat bikes are built with Sram 1x chainring and x5 or x7 rear derailleur. I would like to know if there is an integrated road shifter/brake lever that would be compatible with this rear derailleur (and also mech disk brakes, e.g. BB7). I picture putting this setup on a flared drop bar like a Salsa Cowbell or Woodchipper.