It is really not satisfying to see Milan in this condition. I mean I know they have been trying to fix things recently but they started the national break with a bad result against Fiorentina.

As far as I can see, there are some inner problems there too. For example, in the Fiorentina game Fonseca tried to explain his players that the main penalty taker of the team was Pulisic. But Theo and Abraham took those penalties and missed both...
Fonseca really needs to work on this topic. He should teach his players to respect and obey his choices. Otherwise this team can't be successful much this season. It's no joke.

It is not out of place for a team's penalty taker to delegate his responsibility to another player. But in this case, I doubt if it was Christian Pulistic who gave Theo Hernandez and Tammy Abraham permission to take the missed penalties. They simply dragged the ball and forcefully took the shot. If you watch the second penalty closely, Fikayo Tomori took the ball and gave it to Tammy.
But AC Milan manager Paulo Fonseca has addressed the situation. Pulistic have been warned never to give out any penalty to any player. And I think that's the end of any issues with penalty shots.