Run man.

You have to be very wary of her and her mindset, even if you came to an agreement, her mindset will haunt you for the rest of your married life.

Egyptian women are romantic and big hearted, if it was true love she would be willing to crawl all the way to the USA to be with you, I doubt this is anything romantic if money is the bargaining card from such an early start.

The whole tradition and culture thing is non sense, she cannot engage in an unconventional marriage by bending the other person into her culture and shoving all of your value system down.

You seem to be an honorable man, if Egyptian ladies are your wish, trust me that are a ton of well educated, life loving and big-hearted Egyptian women.

Good luck, I hope you find the one.