Are you allowed to put post-it notes on important quotes for an open-book English exam?
Different teachers have different policies about what materials they allow students to use during an open-book exam. Some teachers will specify that you are only allowed a copy of an unmarked primary text, but many other teachers allow you to use notes. If you are allowed to use notes, then post-it notes are acceptable.
In general, open book tests are essay exams intended to assess your ability to think and synthesize rather than memorization. Thus some teachers encourage you to prepare notes and do underlining and highlighting in your text.
Realistically, though, the guidelines for what you can use during an open-book test will vary depending on the school, teacher, and specific purpose of the exam. The only way to get an accurate answer to this is to ask your teacher.
That is a question best reserved for your teacher. My teachers are fine with it and even encourage it. So long as you're not writing out your whole short answers on little note cards and slipping them into the class, I think you should be fine. Good luck on your test!