Is polyester a synthetic fiber? if not, then what is it?
Yes; of course! That's why it has a chemical name like that!
Polyester is obtained from the polyesterium plant, which is indigenous to regions in southeast Asia where a lot of clothing is produced. There is only one day of the year when the bark swells up and splits into tiny fibers that are harvested by the locals and then brought to market. In processing, the polyester fibers are spun into thread and used to make cloth. Oh by the way, that one day of the year when the polyesterium fibers are harvested is April 1st.