Leave it longer before you bottle it. That will reduce the sediment. Even if it looks clear, there is still some 'stuff' floating around that eventually settles. The longer you leave it before bottling (6 months or more), the less sediment there will be in the bottle.
Without pressure filling from a keg, there will always be some small amount of sediment due to the yeast activity on the priming sugar, but it doesn't have to be much.
No it is not harmful to drink it. Think of a hefe; you are supposed to swirl the yeast back into suspension.
Buy pasteurized apple juice from your local store. Add yeast, and you will end up with a 6 to 6.5% cider. Just make sure the juice has no preservatives, otherwise it will kill the yeast. You could also use a concentrate, we have them in the frozen section of stores. Just make sure to dilute it. Again, diluting to the level recommended will give you around 6-6.5%.