No, we measure the frequency of vibrations of _light_, not of a type of atom. Specifically, it is light emitted by cesium atoms that are transitioning from one specific energy state to another specific energy state. Although this is arbitrary, it is highly reproducible and would give precisely the same measured lengths of time at any point since the big bang.
That assumes that fundamental laws of physics did not change (will not change). This is what we believe and have no evidence otherwise. This is important since we rely on measuring atomic transitions of cesium atoms which itself were formed/forming billions of years after the big bang itself.
The laws of physics invariance under time is a core to our understanding. It would be very disrupting if we found otherwise.
Right, but most deviations one can think of (like, changes over time to physical "constants") would have an observable effect, so ancient galaxies would look much more different from modern galaxies and spectra wouldn't look the same other than a red shift, which moves all the lines in a uniform way.
