"faux bar" is just a marketing term from Specialized. If a bike has 4 members, as in fixed link (frame) moving link one, moving link two, moving link three (might be the rear triangle, or the shock linkage) it's a 4-bar linkage. Both bikes above are 4-bar linkages.
Brake squat can be beneficial during hard cornering, steep stuff, situations where you don't want the weight transfer of braking to be making your front end steeper. It'll get steeper anyway, but not as much as with a "fully active" rear brake.
And yeah, the type of suspension isn't really important, it's the application and how they pulled it off, the shock on there, the tune on the shock, etc. Single ring systems have freed up bike designers considerably, as now you can get good suspension kinematics out of a single pivot bike without virtual pivot points and having to account for 3 possible front chainrings.