Many normal taxis drive also for Uber or Lyft as you need the license anyway over here. Not sure if you can be Uber AND Lyft at the same time.

Payment is preferably cash (I started wearing cash again with how the lovely cashless stuff is ramping up here in the EU), but I had all drivers so far who simply had this Square like device on their phone to take payments. So the driver runs around to let out the 'main' passenger, let's them walk off, runs around to open the van door and tell what the price is cash or tap your card. That is the most common. I see sometimes they charge similar to what the 'main passenger' pays and sometimes less.