7.  A vertical LM curve is often referred to as the "classical case". In what sense is this name appropriate?

There are two answers to this question. 
1. The LM curve is vertical when changes in the interest rate have no effect on the demand for money. This is consistent with the classical model of money, in which interest rates play no role.
2. When the LM curve is vertical, changes in G or T have no effect on output.  This is consistent with the classical view that macroeconomic fiscal policy cannot be used stimulate output.