Electrical – mount a 3 gang box vertically

The 1/16" difference is not a problem. You are allowed up to 1/4" difference. The slight recess is much preferable to the box edge standing proud. Since nothing ever lines up precisely at this level of construction, better to err a little low than a little high.

The flange thickness is also not a problem. It will push the wallboard outwards a bit, but the resulting bulge will occur over a substantial distance, so it will not be discernible to the naked eye. It's similar to the slight bulge when the ends of wallboards are butted on ceilings and then taped over. There is an obvious bulge if you place a straight edge on it. But once everything is finished, an unaided eye cannot see it except with unusually oblique lighting.

These sort of boxes are a great solution to tight installations.

If both switches are of the type 2 configuration in your diagrams, then no. You need unswitched power from somewhere to either the new light or new switch. For example, if either of the switches in the 3 gang box were of the type 1 configuration, then you have unswitched power and can add another switch.

To do what you want you would need to run another conductor from where there is unswitched power available.