How to deal with the unit "Coulomb per equivalent"?
For an electrochemical reaction, you count the atoms / ions by mol, and use the coulomb as a counting unit of charge. For a more intuitive explaination of the $n$ factor in the Faraday equation, try this analogy:

The summer olympics include swimming in a pool with lanes $50\,\pu{m}$ long.  Among the typical competitions are runs about $50$, and $100\,\pu{m}$.  Now, for the sake of the analogy, think the swimmers were representatives of ions.  Each of the swimmers could represent


a $\ce{Cl-}$ to yield $\ce{Cl}$, a change by one unit of charge.  So they swimm only one lane in one competition, $n = 1$; the single discharge happens when the swimmers clap the wall with their hand.
a $\ce{Cu^{2+}}$ wanting to yield $\ce{Cu}$. As they start with two charges now, two discharges in this single race are required ($n = 2$). Their first discharge is when they contact and turn at the opposite wall ($50\,\pu{m}$), their second and final discharge when they clap the other wall with their hand ($100\,\pu{m}$).