1.
An important factor easily overlooked is input impedance. Maybe known and visible in the form of a resistor, or it may be unknown and invisible as coming through a component, IC, power source, etc.
Some amount ought to be included in calculations.
2.
By itself a series inductor slows transitions. Likewise the capacitor to ground. When both are put together they tend to introduce resonant behavior. Thus the oscillations (ringing) as shown in your scope trace. It complicates a formula.
If the incoming square wave matches the resonant frequency, then the inductor slows the leading transition. The capacitor charges and blocks current, causing output to return to zero at about the right moment to coincide with the next transition. It's a handy method to obtain sine wave output.
A circuit simulator is ideal to investigate this behavior.