Looking good, I'm glad you already got Florentbr's s/w installed.
The probe compensation (alignment) only applies for the X10 position on the probes - you will likely see a good square wave on the X1 position because it is effectively a straight through cable rather than a x10 attenuator with resistive and capacitive elements. It would be unlikely (but not impossible) that they wouldn't need a little tweak.
There's really no difference between using the Owon or a bench scope with a properly specified high voltage differential probe for mains use (other that the probe being more times the cost of the scope).
Don't forget to try the FFT function too, it does have one, it works pretty well (the 1022 and the Instek are both 8 bit resolution scopes after all).
The power consumption of the 1022(I) is pretty low - I didn't realize that they ship them with Y cables now. Mine, from several years ago, just came with a single USB-A to USB-A cable and works fine with desktops and laptops. I even bought a longer cable (3m?) cable for occasional use but, while it works, is probably pushing things a bit. Yes, it works fine on USB 1.1