A few lumps in the batter are fine. For the best texture, be careful not to over-mix.
Wait to make the frosting until the cake is cooled, and then once it’s made, immediately spread it on the cake. This is because the frosting starts to set and stiffen immediately because of the instant pudding mix.
For the frosting, either stabilized whipped cream or store-bought Cool Whip work well.
If you want to use Cool Whip, you would need approximately 12 ounces. That’s 1 1/2 of the regular sized containers.