A marriage proposal is an event where one person in a relationship asks for the other's hand in marriage. If accepted, it marks the initiation of engagement. It often has a ritual quality, sometimes involving the presentation of an engagement ring and the formal asking of a question such as, "Will you marry me?" In western culture (or rather the anglo-western culture sphere), it is traditional for the man to propose to the woman while kneeling on one knee before her (occasionally referred to as genuflection), and sometimes putting the ring on her finger, as opposed to merely giving it to her. Often the proposal is a surprise.
No, Mr. and Mrs. Lucas are not happy about Charlotte's engagement.
As it seems they are resolved as Charlotte is that this is the best she can hope for.