No such thing. Any ideology based and unprovable and unverified claims is a mistake by definition.
Given that religion is the root of past major civilizations which we are built on I’d say we wouldn’t have science without it. Hardly a mistake in my opinion. We might still be beating each other in the head with rocks without religion.
You're mistaken on both counts, I'm afraid. Please see http://www.talkorigins.org/indexcc/CI/CI001.html and subsequent pages.
This doesn’t disprove intelligent design. People still argue we are a simulation within science. That’s a form of intelligent design. As is sending a spacecraft that terraforms the beginning of the world and steers throughout history. There are plenty of ways in which a god could have formed us.