We would NEVER use this sentence to ask if someone WILL pay for the breakfast. "Estas pagando" means RIGHT NOW, in the present. If you want to ask about the future you use the future tense "vas a pagar" or "pagarás" is fine. It's unfortunate that half of the lesson about the use of the Gerund makes this same mistake. As a rule, we DO NOT use the "present of estar + gerund" for future actions. That's English use, not Spanish.
Did you not notice the "?" at the end of the sentence ""you are paying for my breakfast?", surly the "?" creates a question. If spoken with rising inflection on the "paying" then the sentence would express surprise, but if If spoken with rising inflection on the "are you" or the "breakfast" then it is a straight forward question. The English language in whatever guise is so flexible...
Why isn't is necessary to include "por" for "for"?
¿Estás pagando por mi desayuno?"
In this sentence the "for" may seem obvious but in a sentence such as ¿Estás pagando mi hijo?" how do you know if it means "Are you paying for my child?" (like for a movie ticket) or "Are you paying my child?" (for doing a task)?
The reason is 'are you paying my child?' (for doing a task) is '¿Estás pagando a mi hijo?'. The child is an indirect object, the money is the direct object: 'are you paying ten dollars to my child' = '¿Estas pagando diez dolares a mi hijo?'. So the sentences wouldn't be the same. Having said that, 'are you paying for my child?' (cash on their behalf) isn't the same thing as 'are you paying for my breakfast?' (cash for the breakfast), unless you're actually buying the child. I think you do need the 'por' if you're paying on behalf of someone, it only disappears in the cash for child scenario.