2) More in general, is there a way to make turn speed faster?
There is an idea of an acceleration curve that remains linear for slow mouse movement (aiming) and speeds up fast movement (turning) several times to provide a faster turn.
Problem with Overwatch at this moment in time is that broken Linear Ramp forces us to compress the linear curve and if we try to divide what's left of the curve into the two zones linear slow and accelerated fast there would not be much left in either the border would be crossed too easily... Or so I suspect.
This is how it normally looks, and would look if Linear Ramp was not broken:
>>> XIM4 [Mouse Ballistics] START PASTE >>>
X4MB:AAAAGgA0AC4AMAAwAC4AMgAwADEANQAwADgAMQA2AAoUHigyPElacIupyMjIyMjIyMjI:X4MB
<<< XIM4 END PASTE <<<

Second option is the one I used in Destiny. Button which doubles or triples sensitivity when held. When I needed to make a sharp 180 I would just press caps lock, and also when sprinting I would keep it pressed to get higher turn speed during sprint.
Third option is "Turn Assist" in the Mouse section. Button while pressed will keep you turning in a direction in which you moved the mouse until button is released.
Fourth option is mapping
right stick to two buttons. Q and E, or 2 and 3. This is done under Keyboard section where you mapped your WASD keys. If 2 is mapped to right stick Left and 3 is maped to right stick Right when you hold one of those buttons you turn at maximum speed in that direction.