For example, if my aunt died and went to purgatory. And I requested Gregorian Series of 30 Masses from Jan 1st to Jan 30th for my aunt. And if someone else also requested 30 Masses from Jan 1st to Jan 30th for that same aunt. Then does it benefit her more to have 2 Masses offered for her each day instead of just one? Or does she only allowed to have 1 Mass offered for her each day?
You can offer as many Masses for one person as you want, but since the benefit of even one Mass is huge, and the Gregorian Masses are supposed to let you have confidence that you did everything you could for the deceased soul, there’s really no need to offer two sets of them for the same deceased soul. It’s not a case of her not being allowed to have two sets of Gregorian Masses said for her, rather it’s that St. Gregory, who developed the Gregorian Mass, would have likely said that two sets weren’t needed.
If somehow two sets did get offered for your aunt, like someone else requested them for her not knowing you already had requested them, then the extra set wouldn’t go to waste because God would just use them to help other deceased souls or to accomplish other good purposes.
A second question I have is: if you don’t want to pay for Mass intention, can you just attend Mass and offer your intention yourself silently during Mass? Or does it better (more merit) if you pay for Mass intention?
As Margaret-Ann said, we don’t “pay for Mass intention”. You are expected to make a donation when you have a Mass said, if you have the money to pay the donation. If you don’t have the money, you can request to have a Mass said for your intention without any donation. In that case they will usually say one Mass for your intention and not make you give a donation. But typically for the special things like Gregorian Masses and Perpetual Enrollments, they would expect a donation as those things involve many Masses being said and special arrangements being made. There is one exception I know of - the
Rorate Caeli Purgatorial Society lets you enroll names of as many people as you want and does not ask for a donation, and priests say Masses for all the names sent in.
You are also perfectly free to just go to Mass and offer your own Mass and communion for the intention. I don’t think that provides less merit or benefit than if you offered a donation to have a Mass said. If I am missing something there, then hopefully the priest or another poster can correct me.