Move events on drag with blocks of 12 hours

Yes, please take a look at the following tutorial:
https://code.daypilot.org/39403/javascript-scheduler-customized-snap-to-grid

Another option would be to change the cell duration to 12 hours using the following settings:

dp.scale = "CellDuration";
dp.cellDuration = 720;

You can use 12-hour cells and still display days in the time header:

dp.timeHeaders = [
  { groupBy: "Month", format: "MMMM yyyy"},
  { groupBy: "Day", format: "d" }
];