Some Problems...
 

So, I bought this Mazda, and the fog lamps dont work, and the driver's side rear door's power locks don't work with the keyless or button. All seemingly minor electrical work, just follow the wires, find the problem, fix it. I just wanted to know if there was anything I should look out for as far as cracking in the electrical system of this car. It's got keyless entry so I didn't want to mess anything up.

Also, the car starts to shake up past 60mph. It'll the front end seems to "wobble" and shake for a bit, then it'll smooth out and ride fine, then you'll come into a turn and if it's above 60mph it'll begin to shake again until the car straightens out and then like I mentioned, it'll smooth out. Also, if you decrease speed below 60mph the shaking stops, but once you regain that speed it will shake again. I had a similar problem on my previous vehicle, and a front end alignment and a tire balanced fixed the problem. Could that be my issue, or could I be looking at something in the suspension? It's got aftermarket wheels, wrapped in 190x50R16 tires.

CF:
The vibration that comes at a certain speed hen goes away is most likely an imbalance of one tire. So have the tires balanced and the wheel bearings and steering linkages checked. You could also rotate the tires and see if the shake moves to the rear axle.
I think you have the right idea about the electrical issues.

Good luck!