How does the Monte Carlo method work on the example of the game tic-tac-toe?

Question

Algorithms

I can't understand a few things:
What to do at the very beginning when there is only one node?
What fields should children of a node have? (I think Move, number of wins, number of games)
First two bots have empty trees. They start making random moves, thus completing the tree. Until when should this continue? Or does he always have to make random moves? Maybe introduce the probability of making a random move?
Should I write down the opponent's move in the tree?