Sand is not an infinite resource. It's crucial for both protection (if you remove all the sand from the beach, there will be nothing to cushion the waves and currents and etc. and it will result in more erosion, which can be deadly for any constructions nearby) and construction.
As such, it's completely normal that you can't just take sand or stones from many beaches. The very famous Étretat town in France with its accompanying beach and rocks, have a very strict "don't take souvenirs from the beach because you'd be actively destroying it" policy.
Sometimes someone has paid money to place the sand at the beach because it wasn't a sand beach from the start. So no, you can't go fill your sacks with sand anywhere you like, not even in Sweden were we can pick berries in the forest for free. Stones, trees and sand is not allowed without permission.
Not particularly, it's prohibited in US National Parks, National Historic Sites, National Memorials, National Wildernesses, National Seashores & Lakeshores[0], US National Wildlife Refuges [1], Most US State parks.
Canadian National Parks[2] and most Provincial/Territorial Parks.
So like less than a tenth of one percent of the US coastline. Literally so uncommon in the US I'd have to go well out of my way to find a section of beach where this is applicable.
Literally none of that is illegal at any of the beaches I've been to (east coast US). Not only does nobody care, there's frequently nobody around to even notice in the first place.
