Percentages involving Finances: Profit, Loss, and Discount

A cake shop sells cupcakes and profits at a percentage of \(80\%\) on the cost of raw materials. The cost of raw materials then decreases by \(20\%\), thus the cake shop offers a discount of cupcake at \(10\%\) for \(10\) days. Then the cake shop retrieves the marked selling price while the cost of raw materials does not change.

1. Find the percentage profit of the cake shop during the discounting period.
2. Find the percentage profit of the cake shop after the discounting period.
3. The marked selling price of each cupcake is \(\$18\). The cake shop sells \(120\) cupcakes on average every day during the \(10\) days of discount. After retrieving the marked selling price, the cake shop sells \(85\) cupcakes on average every day for another \(10\) days.
   Find the total amount of profit of this cake shop during the \(20\) days, considering only raw materials as the cost.