What is the step response curve of a second order low pass filter? And what if it is set for resonance?
I can help with some of your multiple questions. First, a cascade of n buffered RC low pass filters (LPFs), a so-called n-th order synchronous LPF, has the impulse response and step response shown in the screenshot below:



This is a screenshot from my paper 1 referenced at the bottom. All R values are the same and all C values are the same. Buffering simply means there is a unity gain buffer between each filter and on the first input and final output as well. So no filter is loaded or gets loaded. Notice that the conventional unit step function goes from 0 to 1, so if you want the response to be 1 to 0, just subtract y(t) from 1. Then you can find 1/e times as a function of n, etc.

With regard to the four "time = ..." equations you give, only the first one, for n = 1, is correct. In general, second (and higher) order filters do not all behave the same. The simple RC LPF is the first (primitive) member of several filter families. But things get much more complicated (and useful) as the various properties of the filter families are taken into account and utilized.

Note that a cascade of RC LPFs cannot have overshoot or undershoot. On the other hand, Butterworth LPFs can have "ring" in response to a unit step input. This is nicely illustrated by the following figure from Blinchikoff and Zverev 2:



References:

1  E. Voigtman, J.D. Winefordner, “Low-pass filters for signal averaging”, Rev. Sci. Instrum. 57 (1986) 957-966.

2  H.J. Blinchikoff, A.I. Zverev, "Filtering in the Time and Frequency Domains", Wiley-Interscience, John Wiley &amp; Sons, NY, ©1976, p. 114.