Some recipes call for the steeping of specialty grains. These grains will add some flavor, color, and body to your beer. Many people brew with extract + specialty grains because steeping grains is relatively easy, you just let them sit, in a bag, for 15 minutes at ~150F before you add the extract the boil.
I have found the best way to cool the wort is to put it, in my brew pot, in the bath tub with ice water. Cover the pot, open it and stir occasionally. My last brew I was able to cool in 10 minutes. You want to do this as quickly as possible as to not let any bacteria or wild yeast get into the wort. You are having trouble cooling it because the plastic bucket is a better insulator than the pot. I usually cool then pour the water in on top of the wort vigorously to aerate.