“They run into each other.”
Run into someone means to meet them by chance. Although it can literally mean collide while running, with people it often describes an unexpected meeting. Each other makes the action mutual: the two unexpectedly meet again on a street corner.
“No way!”
No way! expresses surprise or disbelief, rather than a lack of a method. Tina reacts to unexpectedly meeting Frank. It also appears in A2-31.
“You're buying.”
Buy can mean to pay for someone's food or drink. You're buying. means “You're paying for us.” To offer to pay, say I'm buying. or It's on me. Delighted at their reunion, Tina jokingly makes Frank pay for the coffee.