Does AC phase shift violate Ohms law?
The input sine voltage is 100V and we know that inductor causes voltage to lag 90 deg behind the current.
My first question is does the phase shift happen in the whole circuit, or only after/before the inductor?

The current through the entire circuit lags the supply voltage. The voltage across the inductor leads the current.

My second qustion is if we would measure the the voltage and current flowing through the resistor R1, and since they are not in phase, doesn't this violate the ohms law ...

The voltage across the resistor is in phase with the current. The amount by which the current lags the supply voltage is determined by the combined effect of the resistor and the inductor.