What is the little dot on some pieces on the board?

That is a marker that shows where was the last move.

What does the dot on the big pieces in the score area mean?

That dot marks whose turn is this, the player that must play next.

Why does Reverso take so much time to make a move?

To play effectively, Reverso includes a sofisticated artificial intelligence that tries to plan ahead so as to choose the best move to make. So, when choosing the next move, it evaluates hundreds of millions of board positions. This is why it takes some time, more time when it must play harder and therefore evaluate more moves ahead.

Sometimes Reverso seems to freeze and do nothing. Why?

When a player, human or computer, cannot make a move, the other player must play again. The computer does that automatically, but the human player must make another move. The marker on the piece of the next player can be used to know whose turn is this.

How can I setup a position?

If you are playing against the computer, but want to start from a given position, just set both players to "human" and play until you reach the desired position. Then set the second player to "computer".