] Also what was the huge deal of Elinor asking Marianne if she was engaged? After all doesn't a mother or sister have a right to know what her daughter/sister is doing, especially when comes to something life changing like an engagement?

Marianne has been acting like she is engaged - if she is not, then her behavior might be labeled as something less than desirable.

If they ask her, they are calling her behavior into question. Even discussing it shows that they have some doubt of the engagement - if she were engaged, she would have told them, right? But in the back of their minds, they can see Marianne reveling in the romance of a secret engagement.