The hop pellets are not supposed to dissolve into your wort. Rather, the boiling isomerizes the alpha acids in the hops (and the isomerized alpha acids will dissolve into the wort), giving the wort its intended bitterness. However, it is totally normal to get an "oil slick", film or foam of hops on top of the boiling wort.
Hops have three purposes: bittering, flavoring, and giving aroma. As a broad generalization, hops added at the start of the boil and up to 30 minutes before ending the boil primarily add bitterness, hops added at 15-30 minutes are primarily intended to add flavor, and hops added in the last 10 minutes of the boil and later add aroma. Of course, the actual bittering, flavoring, and aroma effects of hops depend on many things, including the specific gravity of your wort, the actual "load" and composition of alpha acids in your specific hops, and time/intensity of boiling and cooling.
In your recipe, your first Columbus hop addition is mainly for bittering, the second Columbus hop addition is mainly for flavor, and the last Cascade hop addition is mostly for aroma.
In terms of where the hops end up, most brewers try to leave behind as much of the hop sludge and hop pellets as possible when they move the wort to the primary fermenter. It is a judgment call as to how much wort you are willing to leave behind in the boil kettle. I don't think it will hurt your beer if a little trub (sludge) gets into the fermenter -- it tends to settle out fairly quickly anyway.
Good luck with your first brew!