Jose,
I am just going to give a quick reply to the first issue.
It looks to me like there is a problem with the calibrator output. I think you have another scope so can you feed the calibrator output into the second scope. I looks like there is some noise on the calibrator output just before it switches - both from high to low and from low to high. I would try pressing the 1kHz / 1MHz switch many times while displaying the signal on the second scope. While at 0.2msec/div see if you can make the trace move sideways by adjusting the trigger level control, it may be that the scope is triggering from the first 'noise' pulse rather than the main low-high transition.
Looking at your pictures and even allowing for some over-exposure effects you seem you seem to have the single trace both high and low at the same time which is a physical impossibility, hence my suggestion of noise. This could also explain why the scope seems to be triggering around the half-way point at 0.2msec/div.
More later!
Regards,
Roger
