When all players (or all except one) are "all-in" before flop, is necessary to burn cards also before turn and river?
Yes. You must burn a card every street, I.E. before the flop, before the turn and before the river.
Burn cards are burned in live poker to prevent cheating. If somebody spies, loads the deck or otherwise has an idea of the order of the cards then burn cards help mix it up and make cheating more difficult.
Mostly, it is a deterrent so that people don't think they can get away with cheating. This also prevents conflicts about loaded decks etc that could occur easily without burn cards in play.
The game play of a particular hand itself is irrelevant.
Agree burn the turn and river serves no purpose if everyone is all in preflop. If the card is marked that information is of no value as betting is over. But it is still the rule. In a home game you are free to modify the rules.
Same thing with running the board multiple times. Burning the card serves no purpose as betting is over but they still do it.