For the past week my car has randomly started to vibrate, almost like the engine is revving. It gets louder and I can feel my steering wheel shake. The heat gauge goes up about 3 notches. It lasts about 20 seconds and then goes back to normal. It happened probably five times today. Two or three times I have turned the car on, put it into gear, and then it dies. The ABS light is also on.
Without being there to feel it, it sounds like you might be hearing the radiator fan. They run more at low speeds and less at higher speeds when normal air flow is sufficient to cool the radiator. If the temperature gauge continues going higher than normal, the engine should be checked for a leaking head gasket. Your mechanic will use a glass cylinder with two chambers partially filled with a special dark blue liquid. Air from the radiator is drawn through the liquid while the engine is running. If the head gasket is leaking into the cooling system, the liquid in the cylinder will turn bright yellow.
As for the anti-lock brake light, there will be a diagnostic fault code stored in that computer. A scanner is needed to retrieve the code. GM has been having a huge problem with front wheel bearings. In as little as 15,000 miles, the bearings develop a little looseness which is normal, but that allows the sensor to stop producing a wheel speed signal. Instead of the much more reliable sensor that's bolted to the steering knuckle, GM uses one that's built into the bearing so you have to buy a very expensive part to get the sensor. The good news is that bearing assembly is a lot less expensive than the same bearing without the built-in sensor.
A second problem is sometimes there are diagnostic fault codes that will not be recorded when other codes are already in memory. As an example, when a code is set for one wheel speed sensor, the computer knows it can't rely on that one to compare it to one by a different wheel so there could be a problem with a second sensor but there will be no indication of that when the mechanic reads those codes. Once the first problem is repaired and the codes are erased, the computer is able to detect other problems. That is why it is real common for someone to give you an estimate for repairs, perform the work, THEN find out there are other problems that will cost more money. Typically that happens when the warning light is ignored for a long time, as in weeks or months. If the problem is diagnosed as soon as the light comes on, there won't be time for that second or third problem to develop.