and just how are those plastic bottles recycled, that is by what energy?

I don't know specifically. fossil fuels are involved, but it takes a lot less energy to recycle plastic than to make it from scratch. there is probably no reason why we can't use wind, solar and hydro in lieu of fossil fuels when the need comes.

Polyethylene terephthalate may be pressure-cooked with methanol, and the monomers recovered in methylated form. This represents a savings over making new ethylene glycol and terephthalic acid. The process does require some chemistry, of course.

As far as I know, PETE is the only manmade polymer which is recoverable in this manner. Other plastics can only be "downcycled" into higher-entropy materials such as road surface, wood substitutes, or fuel. And PVC pipe is downright nasty as fuel (phosgene, dioxins and such...)