What version are you running? I seem to remember the tooltip problem being fixed at some stage but it doesn't seem to work when I test it. The AM Charts documentation Tooltips – amCharts 4 Documentation says that the auto left / right feature is enabled since its version 4.
You have the chart hammered up against the right edge of the view so any CSS overflow is going to run off the edge. I'd allow some air in there with the padding / margin settings.
You might solve the problem by splitting the tooltip text onto two lines. I documented anything I have discovered on this thread: Perspective XY Chart xAxes tooltip text {dateX}