clarifications needed regarding monopoly

Might seriously sound dumb questions but -why exactly is MR of Monopoly below its demand curve -why MC is not its supply curve?

Because the price the monopoly charges is always above Marginal revenue. when a monopoly decrease the price, it incures a loss on the price line and a gain on quantity sold, so MR equals total revenue gain - Loss in (due to a price reduction). So the increase in revenue is less than the price by consequent MR is below D -why MC is not its supply curve? Bevause the MC the cost at wich the monopoly is always below the price. And it makes sense, since the monopoly always sell at a price above his MC.