Could you technically write a different Common App essay for each college? Not that I’m going to do that (gosh no) but I wrote multiple drafts and I find that one fits these colleges and the other fits the others etc.
Yes, you can change your essay for each submission. Just be sure to proofread your final application each time to ensure you don’t submit College A’s essay for College B.
Yes, you can, although I’m hard pressed to think of an example as why one would want to. The prompts for the 650 word essay are broad enough to not really need specific college mentions within. Generally when a college wants to know something more specific about you and/or how you will fit in with the college, it will have supplementary questions.
But if you do decide to do multiple versions, quadruple check that you are sending the right version to each college.