A thing cannot, in the same respect and in the same way, move itself: it requires a mover.

This is a false premise. Some things move themselves. You probably want to argue that a god can, for example.

An infinite regress of movers is impossible.

This is a false premise. Infinite regresses happen empirically to not be evident, but are not logically inconsistent.

This mover, everyone calls God.

This is a false premise. Honest people don't declare knowledge of things they can't demonstrate.

Everything that is caused is caused by something else.

This is a false premise. Some things cause themselves (at least in the sense you are saying). Some things (such as the universe perhaps) are uncaused. You probably want to argue that there exists at least one thing (a god perhaps) which exists without being caused. This means you cannot assert that everything (such as the universe) has a cause.

An infinite regress of causation is impossible.

This is a false premise. Infinite regresses happen empirically to not be evident, but are not logically inconsistent.

This cause, everyone calls God.

This is a false premise. Honest people don't declare knowledge of things they can't demonstrate.

Many things in the universe may either exist or not exist and are all finite.

This is a false premise. The universe is by definition the set of all things that exists. Everything in the universe exists. It has no other option. Everything not in the universe does not exist. It has no other option. Whether or not they are finite is also an open question, but it appears that non-finite things cannot exist, including gods.

It is impossible for everything in the universe to be contingent, for then there would be a time when nothing existed, and so nothing would exist now, since there would be nothing to bring anything into existence, which is clearly false.

This is a false premise. If everything was contingent, it would be impossible for there to ever be a nothing. There would always be a prior thing, which is the cause of the next thing, and it too would have a prior thing. No thing would thus be left without a cause.

We call this being God.

But honest people do not.

Varying perfections of varying degrees may be found throughout the universe.

This is a false premise. Perfection is subjective opinion.

These degrees assume the existence of an ultimate standard of perfection.

One should avoid assuming false things.

Therefore, perfection must have a pinnacle.

Consider the vertical asymptote, please.

This pinnacle is what we call God.

But honest people do not.

All natural bodies in the world act towards ends.

False premise.

These objects are in themselves unintelligent.

Most are, at least.

Acting towards an end is a characteristic of intelligence.

No it isn't.

Therefore, there exists an intelligent being that guides all natural bodies towards their ends.

This doesn't follow even if your previous premises were true.

We call this being God.

But honest people do not.