Yes you can, I turn on Uber Driver every night on my commute home from work and they only give me riders heading in the same direction. You can do this up to twice a day on Uber.

You certainly can, at least in some of their markets. The vast majority of my Uber/Lyft rides are carpool rides, frequently there are 3 of us in the car with the driver.

It's called Uber Pool, and Lyft Line.

"Ride sharing" is a common term for Uber and similar companies because when Uber first started you did, indeed, share rides.

Now it's more correct to call it a "ride hailing" platform, but the original term still sticks.