As I remarked in a comment, the interesting question is (3): how might $R^2$ and the point biserial correlation (p.b.c.) coefficient be related? In fact, all three questions will be answered in the following analysis.
We need formulas for the terms that go into computing $R^2$ and the p.b.c. coefficient, but since this focuses on a pair of variables $(X,Y)$ in which (say) $Y$ is binary, these formulas ought to be simple. As usual, code $Y$ with values $0$ and $1.$ (The particular values don't matter, because correlations do not change when values are shifted or rescaled, but this set of values is conventional and easy to work with.)
Following Wikipedia, adopt the following notation:
$n_0$ is the number of observations for which $Y=0$ and $n_1$ is the count of observations for which $Y=1.$
$n = n_0 + n_1$ is the total number of observations.
$\bar X = (X_1 + X_2 + \cdots + X_n)/n$ is the mean of the $X$ data.
$\bar Y = (n_0\times 0 + n_1\times 1)/n = n_1/n$ is the mean of the $Y$ data.
Similarly, $M_0$ is the mean of the $X$ data corresponding to values where $Y=0$ and $M_1$ is the mean of the $X$ data for $Y=1.$
$n s^2 = (X_1-\bar X)^2 + (X_2-\bar X)^2 + \cdots + (X_n-\bar X)^n$ makes $s^2$ the (empirical) variance of the $X$ data (not the unbiased estimator!).
I will write $s^2 = \operatorname{Var}(X)$ and $s = \operatorname{SD}(X)$ as a shorthand.
The residuals are the values relative to their means: $X_i-\bar X$ for the $X$ data and $Y_i - \bar Y$ for the $Y$ data.
The empirical variance of the $Y$ data is $$\operatorname{Var}(Y) = \frac{1}{n}\left[n_0(0 - \bar Y)^2 + n_1(1 - \bar Y)^2\right] = \frac{n_0n_1}{n^2}.$$
The empirical covariance of the $(X,Y)$ data is the mean product of the paired residuals. In $n_0$ of the cases the $Y$ residual is $0-\bar Y=-n_1/n$ while in the remaining $n_1$ of the cases the $Y$ residual is $1-\bar Y = 1 - n_1/n = n_0/n.$ Consequently, $$\begin{aligned}\operatorname{Cov}(X,Y) &= \frac{1}{n}\left[ n_0 \frac{-n_1}{n}(M_0 - \bar X) + n_1 \frac{n_0}{n}(M_1 - \bar X)\right] = \frac{n_0n_1}{n^2}\left[M_1 - M_0\right].\end{aligned}$$
The point biserial correlation coefficient is defined to be
$$r_{pb} = \frac{M_1 - M_0}{s}\sqrt{\frac{n_0n_1}{n^2}} = \frac{\frac{n_0n_1}{n^2}\left[M_1-M_0\right]}{s\,\sqrt{n_0n_1/n^2}} = \frac{\operatorname{Cov}(X,Y)}{\operatorname{SD}(X)\operatorname{SD}(Y)} = \rho(X,Y)$$
where $\rho$ is the Pearson correlation coefficient.
Because $R^2(X,Y) = \rho(X,Y)^2$ (see the formulas at the end of https://stats.stackexchange.com/a/579154/919, for instance),
$$r_{pb} = \rho\quad \text{ and }\quad R^2 = r_{pb}^2 = \rho^2.$$
Incidentally, as you may check, whenever all the data are in one group ($Y=0$ only or $Y=1$ only) all three quantities--$R^2,$ $r_{pb},$ and $\rho$--are undefined.
