1. "Write like a monkey". Meaning and why monkey?

Harvey was arguing with his opponent's counselor for a merger deal. The counselor happened to be his old classmates in HLS. 

Harvey: Is that a joke? Am I laughing? Look, I may not have been awake during our M&A clinic.
Dana: Except for when you were copying my notes.
Harvey: Which was no walk in the park. **You write like a monkey.** But in any case, due diligence is a requirement.

I couldn't find the usage from most dictionaries, but I guess it meant Dana could write very quickly. If I were right, why monkey? I couldn't find the etymology either.

2. "Burning bush" meaning

Mike found himself hard to follow Louis' and Harvey's orders at the same time. He didn't know who he had to listen to.

Mike: I'm still working on Harvey's case.
Louis: Jerome Jensen can go screw himself for all I care.
Mike: But Harvey explicitly told me 
Louis: I don't care if a **burning bush** told you, Mike.
The only commandments you need to focus on right now come from me.

For this one, I found that it can be a bushes with bright, red, autumn leaves or it can be some kind of sexual innuendo. Neither of the two fit. I think burning bush here means something imperative.

3. "Paddle his bottom" meaning

Jessica, Harvey, and Louis were in some hotel's open bar, possibly meeting up with some potential clients. Harvey and Louis were arguing with each other over some trifles.

Jessica: Okay, boys. You don't want me to give you a time out, now do you? Harvey: I'd be willing to stand in a corner, if you agree to **paddle his bottom**.
Louis: Oh, that's hilarious.

Why use the verb "paddle"? Does "paddle his bottom" here mean for Jessica to give Louis a lesson or to reassure Louis. Since I found in Merriam Webster that "paddle" can mean "caress".