Why is the Milky Way and all other spiral galaxies spinning in a way and not the other? What induces rotation?

The planes and directions of rotation of galaxies throughout the universe seem to be random, depending on the initial conditions out of which the galaxies formed. There is no favoured angle or direction of rotation.

Any time a charged body moves, that is an electric current and it produces a magnetic field. Any time an electric current meets a magnetic field the current will be moved. The motion, current, and field all happen at right angles to each other, which we symbolize by a thumb, first finger and second finger. If a current only interacts with its own field the two will continue in a common direction but spiraling around each other. So any time a charged body moves there will be rotation, without regard to any other effects.

That is why everything in the universe rotates, and also how you get jets from a galaxy to go perfectly straight for a half million light years or so.

? They simply are not.

The spin changes with perspective. If a galaxy seems to be spinning counter clockwise, then when you move to the opposite side, it will appear to move clockwise.