No, it really isn't. As I keep pointing out, it's possible to be both agnostic and atheistic, only one, or neither agnostic nor atheistic. See below.
That would be more properly called a Deist. They believe that reason and empiric observation is enough to prove the existence of a god, therefore invalidating things like miracles and organized religions in general. Atheism is defined as rejection of theism in it's broadest sense (the existence of a god). Agnosticism is defined as belief that it's impossible to know if a deity exists, but doesn't reject that possibility. An atheist believes that there's no God. An agnostic believes that we can't really know that.
That's wrong on pretty much every count.
Agnosticism is defined as belief that it's impossible to know if a deity exists
No. Agnosticism is defined as a belief that one doesn't know whether or not God exists. Strong Agnostics further believe that it is impossible to know. Weak agnostics believe that no one knows now but that the question may one day be answered.
That would be more properly called a Deist. They believe that reason and empiric observation is enough to prove the existence of a god, therefore invalidating things like miracles and organized religions in general.
No. Basically all deists are agnostic theists but not all agnostic theists are deists. Especially if you're limiting deism to classical or modern deism.
An atheist believes that there's no God.
No. An atheist doesn't believe in God. I know that sounds like a nitpick but there's actually a very important difference. The lack of a belief. Someone who has never heard of god would be an atheist. Some atheists may go further and actively disbelieve in God but this derives from the lack of a belief in god.
I know that both versions of the definition are used all the time, I've probably used the same one you have. But if we're defining what an atheist is, let's get it correct!
Also note, those terms are not religions in their own right, those are merely beliefs. For instance, an Atheist can also be a Buddhist, especially if we're talking about deeply philosophical Zen (that roughly describes my beliefs, BTW).
While true, I really wish people wouldn't do that. It makes an already confusing topic even more confusing.

Same has how although Buddhism isn't technically a religion, it makes more sense to include it with the religions.