What is this star shaped symbol on the tarmac?
That is a Compass Rose, painted on a Compass Calibration Pad. It's used to mark a location on the airport surface that is suitable for calibrating the compass of an aircraft.

Here's one in a slightly different style:


and a more basic one from an FAA diagram:


More information on the requirements for the compass rose / compass pad can be found in AC 150/5300-13, in Appendix 6.