Is "belép" actually used as "to enter"? And is "lép" actually used? Because in English I can't think of many situations I would actually use "to step".
Yes, and yes.
"To step" is "lépni". The noun version is "lépés".
"One step forward, two steps backward" - "Egy lépés előre, két lépés hátra"
"A small step for me..." - "Egy kis lépés nekem..."
"Please step forward" - "Kérlek, lépj előre"
To enter/join a group, to become a member, is also "belépni".
To just generally enter a building or other place is more generally "bemenni". But when you "make an entrance", that is, when it is a little bit more emphasized, you can say "belép".
Imagine a guided tour of some castle, and the guide says "As we enter the next room..." or "As we step into the next room..." - "Ahogy belépünk a következő szobába..."
You can also "lép" in chess. "I make a move" - "(Én) lépek".
A chef is a boss and a cook a cook. Maybe you mean a chef cook/chef de la cuisine?
I think a chef cook is called a chef. :) According to the internet, "a professional cook, typically the chief cook in a restaurant or hotel".
A "szakács" is just a general cook, not necessarily a chef.
The word "chef" has been magyar-ized, you can use it as "séf". Or you can say "főszakács" - main cook.
As far as I know, is a chef a leader, kind of boss and that there are chefs in all kinds of professions, not only in the kitchen. Is it possible, that it is only in Hungarian, that the chef is only used for the kitchen boss?
I think you are mixing it with "chief", or with some other language. As far as I know, a "chef" (without an "i") is definitely a cook in English. And in Hungarian it is most definitely a leading cook.
Yes, as a native English speaker, "chef" only refers to cooking professionals.
Ok, that's it, thank you! In German and French a Chef is a leader/boss. Now I learned, that in English, hungarian and maybe italian too, it is the boss of the cooks. I am not sure, if Chef can be translated with chief. But a chief inspector is a Chef Inspektor in German.