We have what is termed a transaxle. That is because the differential is encased within the transmission. On a front engine/rwd car, the transmission and the differential are separate units with the transmission attached to the tail of the engine, and the differential in between the rear wheels.
A differential is needed because the inside tires turn at a slower rate from the outside tire, since the outside tire travels a greater distance (think of the larger radius the outer tires must travel). Without a differential, both tires would be turning the same speed all the time, so in a corner, the tires would be fighting each other for grip, since neither would be turning the proper speed for the distance traveled through its arc. The differential usually uses a set of planetary gears that transfer power to one of the axles, rather than that axle being connected directly to the same gear that drives the other axle. It is rather complicated, but once you look at a diagram, it will make more sense.
As for limited slips, there are any number of designs, some mechanical, some viscous (thick liquid). Regardless of the method, the idea for all is the same, to keep the power more evenly distributed to each drive axle. Without a limited slip, one wheel can lose traction (ice, for instance) and spin using all the engine´s power, even if the other tire has plenty of traction. If you have ever done a hard launch in the wet, or given it too much power while exiting a corner, you may have noticed only one wheel spinning. Obviously, this is not the fastest way to make forward motion, so in comes the limited slip differential.
Our Escorts do not have LSD, but for some reason, our cars put power down surprisingly well. This is not just my opinion, as I have read several reviews, over the years, that have remarked on how well the GT puts power down. In comparison, I have found that Civics do a pretty silly peg-leg burnout rather easily.
As usual, I am a pretty windy guy, but I do like to help those who ask, by being thorough.
Next post, I will discuss corner weighting and cross weighting, since I just did a little playing with that on mine.
Oh, yeah, it is the differential that causes the wheels to rotate in opposite directions when you have the car elevated. It is a function of the planetary gearset inside the differential.