I haven't come across any definitive answers for front shifting cross compatibility. My gut feeling is that Shimano's current generation of Road Stuff is the stuff most likely to play somewhat OKwith MTB front derailleurs, because it does run on a longer cable pull than previous generations, and MTB stuff has traditionally needed a longer pull than road, due mostly to the lever geometry (a theory given some weight by the fact that for many years Shimano flat-bar road shifters needed to be paired with a specific front derailleur that worked on a longer cable pull than the regular models) but exactly how well it might work I do not know. As mentioned above, Di2 is the most sure-fire way of getting it to work; as long as the derailleurs are paired for either road or MTB (i.e. both Dura-Ace/Ultegra or XTR/XT, but not one road & one MTB) they'll work with any shifters.
SRAM I have no idea about. Traditionally their road & MTB front shifting has been compatible with Shimano, but that's working off older derailleur geometry, so crossover compatibility is highly questionable. Anyway, SRAM could never get their front shifting dialled, which is why they started the push to 1x.......
As far as rear shift systems/ratios/compatibility/whatever, here's the rundown as far as I've managed to discover:
All Shimano up to 9-sp, plus road 10-sp. with the exception of current-model 4700 Tiagra work on the same ratio, so can be mixed & matched in any combination. (1.7:1 actuation ratio, if you want to know; derailleur moves 1.7mm per 1mm of cable pulled).
Shimano road 11-sp. + 4700 Tiagra 10-sp. is another set, on a 1.4:1 ratio.
Shimano MTB 10-sp. is a stand-alone family on a 1.2:1 ratio.
Shimano MTB 11-sp. runs on a 1.1:1 ratio, which probably accidentally is the same as SRAM 8, 9 & 11-sp. MTB gear (12-sp in both camps I don't know about).
As just noted, SRAM 8, 9 & MTB 11-sp. runs on a 1.1:1 ratio (not quite the marketed 1:1, but close).
All SRAM 10-sp. + 11-sp. road/cross runs on a 1.3:1 ratio, meaning it's probably close enough to fudge to an acceptable degree of function with both Shimano MTB 10-sp. and road 11-sp. It also means you can use a "CX" 11-sp. (eg. Force 1) derailleur in a MTB 10-sp. system to extend the cassette range capacity, but probably not with a 2x up front.
As far as hydro brakes go, ALL Shimano road & MTB levers & calipers will work in any combination. The 1st-gen road R785 calipers were nothing more than reprinted M785/666/675 calipers. Those and the reshaped RS785 and the various flat-mount calipers are all interchangeable with all models of road hydro levers, therefore due to the stem of the family tree, the MTB levers as well. You could run 4-pots with road levers if you really wanted to!
SRAM claimed to have tweaked the master/slave cylinder ratio to improve modulation with their road hydro brakes at the expense of a little bit of outright grunt, but it's probable that most of the difference compared to MTB brakes is in the master cylinder, so feel with MTB vs road calipers should be fairly similar.
As always, never ever mix Shimano & SRAM hydro brake levers & calipers due to being designed for different fluids. Even when different systems use the same juice, it's not wise to mix different brand levers & calipers, as they could well use different cylinder ratios, which may adversely affect brake performance.