Why is it not possible for the current in an inductor to change instantaneously?

The current in an inductor cannot change instantaneously because it implies an infinite voltage will exist, which isn’t going to happen. This reluctance to change is because of the energy stored in the inductor’s magnetic field. The current in an inductor does not (will not) change instantaneously.

Can the magnetic flux be zero when the magnetic field is not zero explain?

The magnetic flux is generated when there is change in the magnitude of the magnetic field as well as its direction. If the magnetic field is parallel to the place of the area exposed then the magnetic flux generated is zero when the magnetic field is not zero.

Why is the magnetic flux through a closed surface zero?

Because magnetic field lines are continuous loops, all closed surfaces have as many magnetic field lines going in as coming out. Hence, the net magnetic flux through a closed surface is zero.

What is the current immediately after the switch is closed?

When the switch is first closed, the current through the inductor is zero, because it cannot change instantaneously. This means that the inductor acts like an open circuit, so all the voltage is across the inductor.

Under what condition the magnetic flux linked with a circuit is zero?

When plane of coil is along the direction of field, the magnetic flux linkedwith a coil is zero.

When magnetic lines of force are parallel to a closed surface then the net magnetic flux through the surfaces?

There will be no net magnetic flux through the surface. Here in question it is given that magnetic lines of forces are parallel to the surface so there will no magnetic field lines will pass through the surface.

Why is the voltage across a closed switch 0?

A closed switch should have a resistance of close to 0 ohms, while a load should have a measurable resistance. Using Ohm’s law to calculate the expected voltage drop across a switch you would get 0 volts because 0 ohms times any amount of current would still be 0 volts.

What happens to inductor after long time?

At t=0, a capacitor acts like a wire; an inductor acts like a broken wire. After a long time, a capacitor acts like a broken wire, and inductor acts like a wire.