Lot's of questions... I try my best to answer them, but keep in mind, I always followed him out of general interest, not because I closely followed his clubs, so I might miss some stuff or see things different than for example Bayern fans.
Media: Let's say, they always get an answer. Even for questions that are not directly football related, and for example his "interesting" dressing style always stirred some yellow press interest. That might sometimes even have been too much, on the other hand does it take media attention and pressure away from the players which I generally see as a positive. More critical probably is how close he is to certain media. His girlfriend works for BILD, not everybody at Bayern liked that afaik, because of course this is a setup that is a risk for leaking internal information. But in general I say he doesn't have problems with the media, he just sometimes doesn't know when he should shut up, the little know-it-all
Playing style: He values a high energy style, but incorporates a reasonable amount of possession play. I think a bit like current Klopp is a good comparison. But to a certain degree he is willing and able to adjust the team formation and philosophy. For example while clearly valuing aggressively moving midfielders in general, he decided to drop Goretzka/Kimmich from the German midfield (Goretzka is completely out, Kimmich shifted to RB), who would probably be his dream midfield duo when in form, because they simply are out of form. Now he builds the team around Kroos and about how Kroos does orchestrate matches. Which is a much different style, but can be just as good.
Pressure situations: In general I think pretty well. Remember, he lead Hoffenheim to surviving a relegation battle when nobody expected that to be possible, that was his first Bundesliga job. Sometimes he might talk too much about certain things (see above), but it rarely feels like he lacked answer when under pressure. Especially what happened at Bayern after him (and in the national team with him and how he is dealing with the current Bayern players there) points towards him not being backed properly to make tough calls instead of not knowing the right answers.