Translation:He sleeps while his friend is talking.
Why not "seinem Freund"? My understanding is that "während" may take the dative (or genitive) case [Collins German Dictionary and Grammar], in which case "sein" (nominative) is incorrect.
Because "Freund" is also nominative: "sein Freund spricht". If the sentence was: "er spricht MIT seinem Freund", for example, then it'd have been dative. I hope I've made sense :)
that one friend that keeps talking FOREVER and you're just like, nope
The contemporary version of this sentence should be: "He stares at his smartphone as if he was hypnotized by it... while his friend is talking" ;)
seine also means "his" -- it's used with a feminine noun such as seine Mutter "his mother" or seine Gabel "his fork", while sein is used with masculine (sein Vater "his father", sein Messer "his knife") or neuter (sein Kind "his child", sein Löffel "his spoon") nouns.
"you" is du, ihr, Sie depending on how many of "you" there are and how well you know them.
seinen is used when it describes a masculine noun that is in the accusative case, for example because it is the object of a verb.
Peter liebt seinen Vater. "Peter loves his father."
It's also used in the dative plural: Peter gibt seinen Eltern ein Geschenk. "Peter gives his parents a present."
"your" is dein - euer - Ihr depending on whether you use du - ihr- Sie. Note that all those forms can have additional endings for gender, number, and case as well, e.g. deine, eurem, Ihres.