The current position in the grid (in pixels) is stored in DayPilot.Scheduler.coords object. This value is updated in real time:
var coords = dp.coords; // coords.x, coords.y
You can use DayPilot.Scheduler.getDate() method to get the date/time value.
Current mouse cursor position as date/time (DayPilot.Date object):
var date = dp.getDate(dp.coords.x, true);
Start of the current cell:
var date = dp.getDate(dp.coords.x);