Most, if not all RJs are Cat III capable, but the crew has to also be Cat III certified, and the specific runway has to be Cat III certified in order for a legal Cat III approach to happen. Most RJ airlines do not train or certify their pilots to Cat III standards, so they can only do approaches that the equipment, crew, and runway are collectively certified for. United is 100% Cat III aircraft and aircrew certified and capable, as are most major airlines these days.

Without going into too much detail, the upper Mach limits of an airplane are generally set with regards to Critical Mach Number, which is the mach speed at which a part of the plane reaches Mach 1. That almost always occurs on part of the plane that has some surface that has a shape that causes the airflow to be faster than the actual speed of the plane through the ambient air. On the old 737s for instance, the air would hit Mach 1 around the engine mount struts while the actual Mach # of the aircraft was only about Mach .77 or so. If I remember right, those old -200s were redlined at .80 or so, but by then, it was well into Critical Mach.

Critical Mach is kind of a self-mitigating situation because the drag increases at an even more exponential rate approaching Mach 1 than it does normally, so as a plane nears transonic flight, it takes a lot more "motivation" to keep accelerating.

Regarding tow-in gates, there are some gates, like a few in LAX, where certain planes, like the 757/767, have to keep rolling all the way to the gate because if they stop before getting all the way into the gate, they need too much thrust (break-away thrust) to get moving again, because there is too much danger of hurting the ground personnel and damaging ground equipment.

FAB