Traditionally, NASA vehicles launched from the Cape go into orbits with an inclination of ~28 degrees (the latitude of Cape Canaveral). Russian vehicles typically launch into orbits with an inclination of 51.6 degrees (I'll explain why in a moment).

We can get a spacecraft to any orientation, but when we launch a vehicle, we like to take advantage of the velocity it already has from the rotation of the Earth. The Earth spins fastest at the equator and slowest at the poles. Therefore, it is significantly cheaper to orbit with an inclination equal the launch latitude. Anything else requires a maneuver that uses additional fuel. It takes more fuel to head towards the equator and less to head towards the poles.

Therefore, when NASA and the Russians negotiated placement of the ISS, it was agreed that it would be more economical to put it at an inclination favorable to the Russians. It also allows a lot more Earth observation experiments, since a greater amount of the Earth is traversed.

Now, as to why specifically 51.6 degrees. This seems a little weird, at first, because we know the Russians launch from Baikonur. But if we look up Baikonur on a map, we see its latititude is at about 46 degrees.

But, sometimes rockets fail on ascent. And having a neighbor that could see rocket bodies falling on it as an attack, it becomes prudent to try to avoid flying over that neighbor on ascent.

Launching at an inclination of 51.6 degrees ensures that the spacecraft does not pass over China until it is clearly in space.

For the last part of the question - No, we do not change the inclination of the ISS - we keep it at 51.6.