The solution to both your questions is enough time in the fermenter. One of the intermediate products of fermentation is acetaldehyde which has the taste of cider or green apples. Given enough time the yeast will break this down into alcohol for you. given enough time the yeast that makes the sediment layer will settle out too. I find that 3 to 4 weeks from the time I pitch the yeast until I bottle solves both problems. With good temperature regulation during the fermentation I can reduce that time a bit but it doesn't hurt a thing to go longer either.