Dawg is slang term for friend, or another person that you know in a laid-back matter.
Alex: "Hey dawg is it cool if I crash at your place?"
Nico: "Yeah fine with me dawg"
Alex: "Aight, I'll be at your crib at around 9."
Nico: "Aight bet homie
Z is a form of Russian propaganda. It roughly means "No retreat". It has seen much more public attention since the Russian invasion of Ukraine, where Russian tanks can see the letter boldly plastered on the side of the tank.
Russian tanks often have the word Z plastered on the side.