here đầu bếp slightly sounds like đầu bếm (because it is in front of này). I would consider this to be normal :D We can observe this in Korean as well, the final consonant sound "p" turning into "m" in front of "n" or "m" to make the pronunciation easier and smoother.
Ahhh... Thanks for pointing that out. Its known as "connected speech" and happens a lot in English.
It really needs to pe specific if the definition is a noun or a verb, I read it as "cook this very professionally" like you wanted a 5 star steak
But this happens a lot it gives poor definitions, for the longest time I couldn't figure out if the word bat was a baseball bat or the animal
"đầu bếp" can only be a noun. the verb would be "nấu".
"cook this very professionally" would be translated as "(hãy) nấu món này một cách rất chuyên nghiệp."