In many places, yes. The parents are responsible for a minor and their actions.

As long as he is a minor, he is their responsibility. The age of majority in most places is 18 years of age, but could be higher.

Class d mistominor could get in a lot of trouble the minor and the person of age supplying the alochol, its a ticket and a fine for the minor i believe and jail time for the adult in most places

In most places, with parental permission. And most require the minor to be at least 16 years old. There are some exceptions, and a court order can be obtained for a 15 year old in a few places.

No. One of the primary expectations in those places that will grant emancipation is that the minor show that they can support themselves.