Motor

I think we should also demonstrate the inertia of motor as a reason for high starting current. Say for Boiler feed pump, normally motor is started with discharge valve closed to reduce starting, keeping a little discharge through orifice.

Think of a motor as a generator. When you spin a generator, the faster it goes, the more Voltage you get. So, the motor generates a "back emf" Voltage which opposes the current going through the motor. When the motor gets up to speed, the back emf is almost as high as the applied voltage and the net voltage is fairly low. If you measure the resistance of a motor winding, it is fairly low so you can't use R to limit current.

The induction motor may be viewed as a Transformer with a shorted secondary ie the stator the primary and rotor the shorted secondary.When a voltage is applied the circuit which predominantly inductive there is no back emf and there is a large inrush current.As the emf builds up the starting current dies down.Similar phenomenon takes place in Transformers too.If u go back to your text books it will clearly explain why and how a back emf develops in a circuit.As regards second question why current increases when voltage decreases is answered by the very equation u have stated.V=IR .Now when V decreases I has to increase to deliver the same out put.Similarly if V increases I redcses to Maintain the same power out put.The other effects of Decrease or increase in V and I in a motor is very detailed subject.The motor draws increased current till about 80% rated voltage and then it stalls unless the load is reduced correspondingly.Hope this answers your question.