PCB Thickness Variability
The board thickness tolerance depends on how good your fabrication house is. 10% is a typical value.

As far as controlled impedances, for professional work the actual impedance is specified in order to give flexibility to the fab house to tweak the trace width to achieve the desired impedance. Good fab houses will do a good job on that. Depending on the geometry involved impedance tolerance of +/-10% is typical. Typically the fab house will actually measure the impedance on a special coupon built on the same panel as the PCB or on the actual trace of interest using TDR in order to make sure they met the specification.

For cheap hobbyist PCBs you're left to you own luck. In practice, the impedance may not be that all off, as long as the trace is not super narrow (the narrower the trace, the higher the tolerance).