I not agree with this solution, for me the red bond formed must be a dotted line in the drawing, and the hydrogen atom musn't be represent with a dot. Am I right or not?
You are both correct and incorrect. (And this entirely without superimposition of quantum states!)
You are taking an achiral molecule and performing a reaction in achiral media to form a chiral product. Symmetry dictates that the reaction must be racemic, so there must be equal amounts of upward-pointing and downward-pointing carboxylates.
However, the drawing is also incomplete. It does not make sense to discuss the reaction without labelling the entire stereochemistry at the newly formed bond. It is important to realise that it generates only two of the four possible stereoisomers: the two syn ones ((S,R) and (R,S)). You should add an upwards-pointing hydrogen to the right-hand carbon of the new bond.
Judging by your comments, you are only interested in the arrow direction and resulting movement. Well, the arrows are not clear. They are 2D on a 2D plane and trying to signify a 3D movement. You could grab the curved bit of the arrow like a handle and:
either pull it upwards — then you have a rotation which would move the carboxylate below your screen’s plane and create the downward-pointing product ((R) on the α-carboxylate carbon),
or push it downwards — then you have the rotation which would move the carboxylate above the screen’s plane and create the upward-pointing product ((S) on the α-carboxylate carbon).
So the arrows’ directions are arbitrary, we do not know if the are shaped below or above the plane.