Two good questions. To replace the missing shingles, simply slip the new ones into place where the old ones existed and hold them in place with barbed roofing nails. Roofing nails are short and have larger than normal heads. Two in each shingle is all that you should need. Hold the shingle above up and out of the way and use a flat pry bar as an extension of your hammer to drive in the nails. Be careful not to pry too hard on the existing shingles chances are they are dry and brittle.

It sounds like you have a combination of moss and mildew growing in a shady part of your roof. All you'll need here is a cup of household bleach mixed into a gallon of warm water. Apply the solution with a nylon bristle brush and rinse with fresh water. If the moss is deeply embedded in the shingles you may have to rent a power washer, but try our method first.