I have two questions:
I need an event to register all the movements that are made in the gantt.
How to refresh gantt when data has been change.
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I need an event to register all the movements that are made in the gantt.
You mean all drag drop actions? Or all data interaction? You can find a vast amount of events fired by the Gantt chart here: https://bryntum.com/docs/gantt/#Gantt/view/Gantt#events
If you are looking for data level events, you can learn about those here: https://bryntum.com/docs/gantt/#Core/data/Store#events
How to refresh gantt when data has been change.
If you change data the view is always up-to-date, no need to ever manually refresh it.