Your latest two video’s exercise the scope using sine and square wave signals and the display appears to trigger correctly, presenting a stable display over all the available timebase speeds.
The CRT display is acceptable, given that the scope was designed with economy in mind, as the front panel controls and circuit complexity/component count are very limited.
I note that the trace rotation needs horizontal alignment. In a more expensive scope this would be done electronically, but in this case you need to slacken a clamp on the CRT neck and turn the tube until the trace is horizontal.
The previous problem you identified “Bwd504 2Mhz input square wave issue” where you have a 2Mhz waveform displayed using the 0.5uS timebase and subsequently switch to slightly lower sweep speeds (1uS and 10uS) creates an artefact/artifact or undesirable phenomena, which is probably a consequence of the design economy. The same video appeared to display a 2.0MHz square wave, which is quite an achievement for a scope with a 6.0MHz bandwidth! In reality the scope is probably intended for audio or ultrasonic signal applications.
The latest videos suggest to me that the scope is working, as well as can be expected.