Is it allowed in tennis, to hit the ball two times, without the ball touching the ground?

***I wonder if it would be allowed to hit the ball carefully pointing upwards, so that the ball elevates a few meters, and when the ball falls the player can hit it much harder and without the fear of the net.***

What you describe here is an illegal, double hit.

"Rule 24. PLAYER LOSES POINT

The point is lost if:

...............

f. The player deliberately carries or catches the ball in play on the racket or deliberately touches it with the racket more than once;"

Now, see USTA Comment 24.5:

"Does a player lose a point if the ball hits the racket twice during one swing?

No. Only when there is a definite and deliberate "second push" by the player does the shot become illegal. "Deliberately" is the key word in this rule. Two hits occurring during a single continuous swing are not deemed to be a double hit."

No A player is permitted only one swing at the ball. So you ca nonly swing once at the ball, so if it hit the racket twice like you mentioned it is still legal but you cant set the ball up and then hit it .

Given the speed balls come from one end of the court to the other, it's hardly likely to happen. If you are suggesting a player hits an incoming ball up into the air and then 'smashes' it - I doubt this would be taken as legal, even if possible!!

No, you can only hit it once.

It is illegal.