Mutfak ('kitchen') is more appropriate for describing cuisine than yemek ('food') as in Türk mutfak. (Note, this is Türk, just like a person, not Türkçe. Only the language is Turk-ish.)
Hocam ('teacher') is not a mispronunciation of the jiujitsu coach's name.
I think the word for the cold-plunge pool at the hamam is hozam, but don't hold me to that.
Whereas beraber (as previously discussed) means 'together', birbira means 'each other'.