Why does increasing surface area of the electrode decrease resistance?
Fluid flow is always an excellent analogy for understanding current flow.

Fluid flow rate -> electrical current

Pipe friction, valves and other throttlers -> electrical resistance

Fluid pressure -> voltage.

In this case, the amount of contact between the electrode and the solution is most likely the bottleneck of the circuit so increasing the area of contact should increase the current.  Similar to how cranking the valve on a faucet or outdoor spigot more and more open increases the flow rate of the water coming out.