Question 1: Why is the flywheel of an engine made heavy in the rim?

We know that moment of inertia is

…        (1)

Heavier the mass, larger is the moment of inertia.

Similarly,          τ = Iα

Put equation (1) for I

Greater the moment of inertia, less the angular acceleration. (Both are inversely proportional, as the above equation indicates). Therefore, when the mass is larger the angular acceleration will be less. So, the flywheel is heavy in the rim in order to have the greater moment of inertia. Consequently, angular acceleration is smaller. Moreover,

So, when the flywheel undergoes some change in the kinetic energy, then due to high moment of inertia (I), the change in angular velocity ω happens to be very slow.
The benefit is, obviously, a uniformly rotational motion is obtained. The sudden jerks during starting or stopping a car are prevented.

A flywheel is a heavy metal disk attached to the crankshaft. (a crankshaft is part of the engine that converts the linear up-down motion of the piston to circular or rotatory motion. It is connected to the drive wheels which make the car move.) Due to its heavy weight, a flywheel has more inertia. Therefore, it keeps rotating for a while when the engine stops. In this way it prevents the car from a sudden jerk to stop. Similarly, when the engine starts, the flywheel prevents the engine to run from its final speed from the very beginning. In this way it again, prevents a sudden jerk to the car. So, due to the presence of flywheel, a smooth motion of the vehicle is ensured.