I was a bit surprised by the way the payment is being made here.
Do people pay it separately like this? In general, if it isn't a prepaid restaurant, then just one of us makes the whole payment, and we pay our share to that person.
Don't people follow that generally?
It varies, culturally and based on what the group is. In the UK if I'm out for a meal with family or close friends then one of us will probably pay the bill and then people will offer to transfer their share to the person who did (which may or may not be refused depending on circumstances), if I'm out with colleagues or a group of looser acquaintances then its more likely we'll each pay our share separately, which the server is generally happy to accommodate.
In college I used to go out to eat from time to time with a group of friends to a midnight pancake house.
This was a very nerdy group! In our "culture," everyone wrote down on their paper placemat the exact cost of each item ordered, and at the end of the meal calculated the exact amount of tax plus the canonical 15% tip, and put the correct amount on the table, making change as necessary.
It was pretty fast and frictionless!
That’s not universally the case, no.
For example in Germany, splitting the bill is pretty normal, to the point where restaurants are adapted to it. Since this process adds some friction it is, however, also the case that someone will pay for everything and split afterwards (or variations on that theme).
Newer payment systems seem to have made that easier (e.g. mobile devices that allow waiters to initiate the payment for a subset of what a table had and allow for contactless payment). The older variant of that is the waiter going with you to the cash register that basically allows them to do the same bill splitting. The even older variant is the waiter breaking out paper and pencil and doing some addition (though I seem to remember waiters actually being annoyed if they had to do that, not so with the new solutions).