Is 13 a good age to start learning about unity3d and game designing?
There is no “good age” to start learning thing X. Generally (not always), the fact that you are capable of asking yourself that question says that you are more than ready.
Every single time I’ve tried to learn thing X, I get annoyed that I didn’t try learning it 2 years ago.
I picked up my first programming language when I was 11. I barley used it, but every little bit and piece made things easier in the future when I needed to start programming for school.
The only thing that you should worry about is that you try to act mature when dealing with the public. If you think something could possibly be misinterpreted, IT WILL (avoid potty humor, crude jokes, etc).
While I’m on the subject, Math is good for you! Trust me!
Well, it depends on you. If you passionate about game design, then learn it. But it won't be easy unless you know math. I started learning unity at the age of 15 which is my current age. So, it depends on your feeling.