both, plastics are sorted by type then it gets chopped up into little pieces and melted down. your plastic bottle today might be tomorrows plastic wrap.
At times yes. but you can only recycle a plastic bottle no more than once. then they just even make more plastic which is harmful.
recycled plastic cannot be used in clear plastic bottles and only a small % can be used in other products and some products like fake wood a lot can be used once virgin plastic is used it loses some of its properties and cannot be used in some products at all and there is also different kinds of plastic which can't be mixed
all of the above! (and more) it can be used to make plastic bottles, other plastic items/containers, and even clothes, pencils, jungle gyms, and wood-like material for making benches for parks, decks, etc. the possibilities are endless. :)
Most of the time, no. Plastics are usually downcycled, that is, made onto products of lesser quality and after that, off they go to the landfill. Only HDPE (#2) is recycled into similar products.