With enough live rock and sand, no, you don't need any other biological filtration. Crabs, snails, worms, stars, shrimp and pods act as mechanical filtration, and a skimmer helps with both.
For anenomes, I always encourage metal hallide lighting. Many corals will be okay with the ~4WPG from the compacts, but not all--you'll want to research the corals specifically and go from there.