Triaxial accelerometer to single signal
Your expression $A=\sqrt{a_x^2+a_y^2+a_z^2}$ calculates the length of the 3-dimensional vector with coordinates $(a_x, a_y, a_z)$. So, it is the magnitude of the acceleration. Your expression $a=\Delta_v/\Delta_t$ also gives magnitude of acceleration, but in a slightly different context. This comes from measuring speed at different times, and then you average the acceleration between the time steps. You can ignore this expression for your case.
given ax, ay, az are $N$-dimensional vectors that contain the measurements of $a_x, a_y, a_z$ over time, you would do A=np.sqrt(ax**2+ay**2+az**2) to calculate the magnitude over time.
Yes, it's the overall acceleration at every time point. Though, it is only a relative value, its unit will not be exactly $m/s^2$, but there is some scaling involved to transform your measurement $A$ to the common $m/s^2$ units. Though, you don't need to do it, since you are only interested in relative changes of the acceleration over time. 
Looks reasonable. Just plot $A$ vs time for some steps and decide on your own, if your measurement would contain sufficient information.