A BBP-type formula for an irrational number $\alpha$ in the integer base $b\geq 2$ is a formula in the form $\alpha=\Sigma_{k=0}^{\infty}\frac{1}{b^k}\frac{p(k)}{q(k)}$ ($p, q$ are polynomials in integer coefficients) that allows computing the $n$th digit of $\alpha$ in the basis $b$ directly and without any need to computing the preceding $n-1$ digits of $\alpha$. It is also connected to the problem of normality of irrational numbers.

1- For which irrational numbers do we have a known Bailey–Borwein–Plouffe formula? For which of them do we have such a formula in the base $10$? (Please add a reference to a list if there is any).

2- Is there any known BBP formula for $e$ in an integer base $b$?

3- For which irrational numbers, the normality of the number in a given base is proved using a BBP formula?