Why does equal resistance and capacitive reactance lead to 70,7% of the output signal?
Here's what you assert (correctly): -

\$V_{OUT} = V_{IN} \dfrac{X_C}{\sqrt{R^2 + X_C^2}} = V_{IN}\dfrac{X_C}{Z}\$

Let's take the example of R and Xc being equal in magnitude. What does this make the denominator: -

\$\sqrt{R^2 + X_C^2} = \sqrt{2R^2}\$ (because Xc = R)

Therefore the denominator becomes \$\sqrt2\cdot R\$ and the R cancels with the R (or the Xc) in the numerator hence,

\$V_{OUT} = \dfrac{V_{IN}}{\sqrt2}\$

Pythagorous is the reason why the R term and Xc term are squared - an R and a C do not form a potential divider like an R and an R - the impedance of a capacitor is at right angles to the impedance of a resistor.