1 is always 1. It’s 1 × b⁰ where b is the base. Anything raised to the zeroth power is 1.

10 is the base. 1 × b¹ + 0 × b⁰

That doesn’t make it rational but simply makes it writable in 2 digits(10)

Also you should have 3.1415… “number of characters” in that base… The base becoming irrational will make the number irrational

Writing the same number a different way does not make it rational. There are no two natural numbers p and q so that p/q = 1 base pi.

π = 10

in base 10, 10 = 10.

Even in base π, π is still considered an irrational number; using an irrational based doesn’t change the fundamental identity of whole numbers or irrational numbers, it just changes the way we write them.