Base 10 Number System Question

[boc4life]

I'm trying to understand some concepts behind the Base 10 number system, and I have a few questions.

Imagining a scenario where after the number 9 came the "number" A

1. What would the order of numbers be?
...8, 9, A, 10, 11, 12...18, 19, 1A, 20, 21...

Does that look right?

2. Would this number system be described as a "Base A" system?

3. (Unrelated to the imaginary number system) Why is Binary referred to as a Base 2 system, when the number 2 does not even exist within the system?



Do I appear to be way off in my thinking?