TSM is built into the radio system with a gyro in the receiver. Changing other components won't effect the TSM. But having TSM is useless on a track since it's a drivers aid and illegal in racing. If you're found using it you'll be disqualified, possibly thrown out or banned depending on the track.
Now as for the rest, it depends. Most tracks have amateur or stock classes with limitations on modifications. This is not always the case and it depends on vehicle type. 4wd typically only has one class and that class is modified where to be competitive you need a bigger aftermarket motor and faster steering servo. What if you're ok not being competitive and just want to run can you run the stock motor? If the track follows ROAR rules requiring a sensored motor then no you can't because the stock motor and esc (is sensorless and) doesn't conform to ROAR rules. So you need to ask them if the rules state you must run sensored for the 4wd SCT class or if that was just their recommendation to be competitive. The stock steering servo actually isn't that bad for a ready to run, good torque but a bit on the slow side.
Now for recommendations. First, watch some videos, do whatever you have to do to and learn how to wrench. Replacing a motor is a piece of cake. Replace the motor and esc in your Dominus with a bigger and better setup. Then run it. Get the drive time in, practice on the track, improve your driving skills. The Slash 4x4 may be a step up from the Dominus but it's not the best track weapon in my opinion. Not compared to other vehicles out there.