Uh-oh, here's the religious thing again. Just from memory and unscientifically, as I recall the consensus was, No you can't be an Objectivist and be religious because religion is irrational. However, you can be religious and follow the concepts of Objectivism and be part of the Gulch. My advice, however would be to either drop the religion or don't start arguing religion VS atheism.

I believe many in The Gulch use religion much like the wanderer uses a compass. There is no denying Good & Evil in the world that surrounds us, as there's no denying there's a North and a South. In my opinion, the confusion for many is when that needle points in an Easterly or Westerly direction. This is where many fall back or support their thoughts and direction through the use of religion. (PS: I am a believer in THE higher power...)

Yes if your religion happens to be objectivism.

Yes. Objectivism is defined as the belief that certain things, especially moral truths, exist independently of human knowledge or perception of them.

Firstly, does religion always rely upon the existence of a deity? I can think of several examples where this is not the case.
Secondly, The world as we see it appears to be the consequence of a collection of fundamental and intricate physical laws. Does this imply the existence of a supreme law giver or do we need to re examine what we mean by God?
Thirdly: Atheism is based on a severe logical difficulty, that being finding a proof of the negative of a proposition. As Heinlein observed, "Atheism is just Godism turned up side down."
If a religion is based on a testable set of logically defined axioms would it be anathema to Objectivism?
When in doubt return to what you have accepted as first principals, examine them carefully for hidden assumptions, and then and only then draw conclusions.

Had Ayn Rand been given more time, and the opportunity to experience God, She would have revised her definition of Objectivism. She just wasn't lucky enough to encounter the Creator of the universe, that's all. Everything she was, and all that she contributed to society were gifts from God. Her mortality speaks of her human condition, and that, was determined by the Almighty. Knowledge is a gift from God. Use it!