Is it possible to move resources from warehouse (TOP) to Boxes (bag)?

No, you cannot move them directly. Resources in the warehouse can only be used / spent.

The best you can do is use them to complete the events / hourly challenges and gain reward boxes which do then go into your inventory (bag).

You can accomplish some movement to the bag by trading at the Trading House. Your exchange options are limited, but you can protect some resources this way. Personally, I trade as much ale and charcoal as possible for supplies ... not so much for gold.