1. Book only has that meaning in the expression "book it." Is usually in the context "run away because it's dangerous." Bounce has a few meanings, none of them are very common. When this is used, it usually means "start moving" or "get started."
2. They have the same meaning but the connotation is different. Anxious is bad, you would use this when you are not looking forward to something or you are scared. Eager is good, when you are looking forward to something.
3. Scaremonger is a noun, frighten is a verb. These words do not have a lot in common.
4. Chastise means "to tease, to mock, to do mean things to someone, to say mean things to someone to hurt them." Persecute is "unfair treatment towards someone." An example of persecution would be "These women are not allowed to drive, they are persecuted."
5. They all can mean the same thing. "Let's get going" can mean "to begin something" but is often used to means "let's go to (place)" when the destination is obvious to listener.
"Let's get started" can only mean "Let's begin to do (verb)" when the verb is obvious to listener.
People would say "Let's get (noun) underway" instead. This is the same as "let's get started" but isn't as common.