Aditya, a comment would have been enough perhaps. But I want to end the matter here. So here is a detailed answer.
As for your first question, my second comment must have proven it to be quite irrelevant. I believe you took your teacher too seriously (when he/she mentioned about the "inertia") without checking the Law in detail. I am putting up the comment which serves as my answer and I quote:
Your reasoning is correct but it is a trivial point and moreover it is NOT the law. The law is a direct consequence of the principle of conservation of energy. As you move the magnet, you do some work and the magnetic flux through the coil changes.This work done is manifested in the form of an induced EMF which causes a flow of current and produces a magnetic polarity, attracting or repelling, conserving energy.
So you see, inertia which forms a major part of your first question, is not that important. And the question becomes, to some extent, meaningless.
Now, as far as the second question is concerned, one thing to understand is that the galvanometer arrow gets deflected in the direction opposite to that of electron flow, i.e, in the direction of conventional current. That is how the instrument works- its working principle. Now if you ask me why, I will say you should go and consult the following from any standard physics textbook:
- The derivation of the formula $$\vec F = i(\vec l \times \vec B)$$ that is the magnetic force acting on a wire due to some magnetic field.
- How the above formula is used to derive the relation for magnetic torque, that is, $$\vec \tau = \vec m \times \vec B $$
- And finally how the above formulae are used to deduce the expression for the working principle of a galvanometer.The one I mentioned in the comment- $$ϕ=(\frac{NBA}{k})i$$
If you study these in detail, you will have no doubt that there is no right or wrong direction for a galvanometer arrow...its just that it is made in such a way that it depends on the direction opposite to that of electron flow, i.e, in the direction of conventional current.
P.S. I don't understand why the galvanometer is showing right or wrong direction, i.e. when the magnet is inside, South polarity is induced on the left side of loop and the reverse on the right side. So if you draw the direction of current, it flows from left to right. As the magnet is tried to be removed the induced emf opposes and so the direction of current changes and so does the deflection of galvanometer. And it is not clear on which side of the wire the +ve side of the galvanometer is connected. So nothing can be said about the direction in particular. If the connection is reversed, the deflection is also reversed.
I hope I cleared your doubt.