Even if she was an astonomer, it would have been impossible for her to predict that. There are too many variables to handle—even for the most powerful computer. Not only it would have had to include every particle in the universe, but also how they would affect each other.
In the first sentence, there are two possibilities:
1. Even if she had been an astronomer, it would have been impossible for her ...
2. Even if she was/were an astronomer, it would have been impossible for her ...
In both sentences, the speaker is talking of a past counterfactual situation - the possibility of her being able to predict something. In both sentences, it is implied that it is impossible for astronomers to predict such things.
In #1, the speaker is suggesting the counterfactual past possibility of 'she' being an astronomer at a particular past time. Even that profession (at that time) would not have changed her ability (at that time) to predict whatever it is. Your sentence is therefore possible.
In #2, the speaker is suggesting the counterfactual present possibility of 'she' being an astronomer now (and in the past and future). Even that profession (in general time) would not have changed her ability (at a particular past time) to predict whatever it is.
Your second sentence is fine as it stands - there are too many variables ... in such situations. You could also say There were too many variables ... at that past time
Your third sentence begins with a negative expression, Not only, and therefore S-V inversion is required: Not only would it have ...