Great to hear you're interested in using ShinobiCharts for Android!
In answer to questions 1) and 3), we are currently working on further customisation options for both tick marks and the crosshair which should enable you to achieve the desired effect. While I cannot give definite timescales at this point in time, we're hoping to include these features in our upcoming release, v1.5, which is provisionally scheduled for early to mid June.
In the meantime, for question 1) you may find altering some of the style settings for the category axis' tick marks, such as text size and orientation, will help lessen the amount of overlapping.
With regards to 2) there isn't currently a way to add click listeners to axis labels. For performance reasons we actually favour drawing the labels straight onto the canvas rather than representing them as individual TextViews. We do, however, currently provide a general gesture listener for the chart (ShinobiChart.OnGestureListener) which can hook into single touch events, for example. In combination with this and our upcoming tick mark customisation enhancements you should hopefully have the flexibility you need to achieve your desired behaviour.