Is it permissible for one of the friends to pay for everyone if they ride in a taxi or have a fast-food meal?

It is permissible for siblings to agree that one of them will pay off a debt they owe, on the condition that they will repay him later. If what one of them pays on your behalf is a gift or a reward for a good deed, then it is commendable and he will be rewarded for it. It is not permissible to take something out of embarrassment.