is there such a thing as a mechanical quartz clock? (non electronic)?
What you have sounds like a very basic alarm clock. Push the button in that turns the alarm on and off, that should turn the alarm off. Now turn the alarm set knob while watching the front of the clock to set the alarm time. This is a very basic alarm clock so if you set the alarm for 6 o'clock it will go off at 6 in the morning and 6 in the evening if the alarm button alarm is pulled out(ON).
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Set Alarm For 6 This Evening
A detailed description such as you so carefully provided here unfortunately does no good at all; even a brand and model would not help much, because there are so many different clocks and it is unlikely that any answerer would have one similar to it. Fortunately, most mechanical and analog quartz alarm clocks are set the same way: Shut the alarm off and set the alarm hand to the time you want, then enable the alarm.