Hi! I'm no expert in scopes, but I think there is nothing wrong with your scope. But it needs a bit of probe adjustment and some understanding of how it works (sorry if you waited an answer from Micsig, but got it from me).
1. The measured amplitude and frequency are slightly different across the channels. Is this normal?
For amplitude yes (within 2%), provided we are talking about low freq signals (square wave is _not_ a low freq signal as it always contains high freq components causing ringing and peaking). If probe compensation and matching is not ideal there will be difference. Scope channels are also a tiny bit different. For high-freq signals it gets quite complicated, you need to use special measuring techniques to get accurate results (even putting your body near the circuit or moving a hand can affect measurements). For freq. I dunno, I need to see how you do it. There are two ways to measure freq on this scope (one is using hw counter, another one is by analyzing waveform). Long story short, try to unzoom the picture to fit more periods of your signal and check if measurements more stable and accurate.
2. While the horizontal lines of the square wave on Channel 3 are straight and horizontal, those of Channel 4 are slightly tilted. How come?
Given the freq. of the signal, I don't think it's a AC/DC coupling issue (but I can be wrong, check all channels have same settings). Looks more like you overcompensated the probe on channel 4. May be same for other channels.
3. It looks like a new issue came out which did not happen before. i.e. some horizontal lines became dotted lines. See the two green lines at the bottom (on channel 4) for example. How the lines are dotted rather than solid like before the self adjust?
It's actually how it is supposed to work. Please read about visual persistence in digital scopes, or change settings (like, remove persistence) if you don't like how your waveform is displayed. In short, it displays multiple captures at once. Waveform become wider at places where captures diverse due to, e.g., noise.
4. In Channel 1, the yellow horizontal lines are not very straight.
Overcompensation. You tried to make "square" wave as square as possible, right? But no, that's impossible. Edges cannot be perfectly vertical and nice, no scope can do that. So, you have to find a balance when edges are good-enough and you don't get much other distortions (tilts, ringing, etc).
I skipped answering other questions as they all about the same: probe compensation, measuring square waves, visual persistence, accuracy of scopes and high-freq measurements. I think you can ask in
https://www.eevblog.com/forum/beginners/ to know more about these. Just please do not ask all at once, pick one topic at time
.