Can you dismiss an appeal?

No

Yes, you can appeal it, because the order dismissing a case is considered a final order rather than an inter locutory order, because the dismissal ends the case.

That means the party who appealed is bound by the decision of the lower court unless an appeal to a higher court is possible.

Who do you mean by "the parties?" Only the party that filed the appeal can file a motion requesting that it be dismissed. The opposing party would have to file a motion with the appeals court asking...

The Supreme court