Does B appear as the leftmost digit in the duodecimal (base 12) representation of any power of 2?

Does 9 appear as the leftmost digit in the duodecimal representation of any power of (37)₁₂?

Is it possible to find a power of any counting number that has a given digit as its leftmost digit in the duodecimal system?

Bonus: What percentage of the powers of 2 in duodecimal system have 1 as their leftmost digit?

Note: In finding the powers of "any counting number," exclude powers of (10)₁₂, whose leftmost digit is always 1.