Let us look at these statements one by one.
The reaction is non-spontaneous - yes
The reaction occurring in an electrolytic cell is always non-spontaneous. We need to supply energy in the form of electricity from outside to drive the reaction. This is the basic difference between electrochemical and electrolytic cell.
A potential equal to the cell potential needs to be applied - no
A potential equal greater than the cell potential needs to be applied. If a potential equal to the cell potential is applied, the reaction would just hold at a standstill, neither going in forward nor reverse directions.
The flow of electrons is from anode to cathode - yes always
The flow of electrons is from anode to cathode always. Regardless of whether it is an electrochemical cell or electrolytic cell. By definition, anode would get oxidized and cathode would get reduced.
So, electrons are released at anode always and get accepted at cathode always. This would imply that electrons flow from anode to cathode always.
The flow of current is from anode to cathode - no
If the flow of electrons is always from anode to cathode, the flow of current would always be from cathode to anode. This is by definition and doesn't change.