1) always show a minimum count of labels
As Anna explained earlier, you can use the MajorStepUnit and MajorStep properties of the axis. When you make a selection in the timebar, you need to take a look at the selected range and decide whether the step unit should be days, months, years or else. In the method in which you decide the step unit and the step, you can include logic so that a minimum number of labels is shown. For example if the selected range is 2.5 years and you require at least 5 labels, you should not use Year because it would leave you with two labels, you can use either Quarter or Month step unit.
2) add annotations which show the timespan between the axis-ticks and if possible time elapsed after visiblerange.min
I am a little unsure where you want to add this annotation. You can use the Annotations property of the chart if you need to add chart annotations. The chart annotations are usually some visuals in the plot area which emphasize data and so are data dependent. What you seem to need is not such an annotation, because it is not related to specific data.
You shouldn't have any problems with the content of this annotation - since you manually set the step unit and step, you know what is the distance between two ticks.
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