Learn German: Gestern war ein Sturm. Darum ist das Fenster kaputt. - Yesterday there was a storm. Therefore the window is broken.

Darum is an adverbial connector that takes up the first position in the sentence. In German, the verb must always take the second position. So, the verb ist comes right after darum, which pushes the subject das Fenster into the third position.

Could I use deshalb or deswegen instead of darum here?

Yes, absolutely! Darum, deshalb, and deswegen all mean the same thing: therefore or that is why. They are completely interchangeable and follow the exact same word order rule. You could just as easily say Deshalb ist das Fenster kaputt.

Why is the first sentence Gestern war ein Sturm instead of Gestern ein Sturm war?

This is the exact same verb-second rule at work! The time word gestern takes position one, so the verb war must take position two. This pushes the subject ein Sturm to position three.

Is kaputt the best word to use for a broken window?