I'm almost sure that if you ask a Persian speaker, he/she would tell you that the first sentence sounds a little bit odd, but not wrong. And actually, it's not wrong. Because با can mean either 'with' or 'and'. In case that it means 'and', it changes its role from preposition (which is usually 'with') to a conjunction (which is 'and'). Therefore it depends on how you're dealing with the subject here (او=u). Consider this example: He went there with Ali 1. Ali accompanied him: او با عَلی رَفت 2. He AND Ali went there: او با علی رَفتَند or او و عَلی رَفتَند (Source to check the role change for با: Moein Persian Lexicon)

"u ba khaanevadeash dar daneshgah zendegi MIKONAD". Absolutely "mikonad" is correct and you are right about that. I do not know why your textbook says a wrong sentence! Be successful

I think you are right, sometimes when the sentence becomes too long, it might get a little tricky to keep the agreement between the subject and the verb. in your sentence for you example if we remove the part "در دانشگاه" from the sentence, it becomes crystal-clear that "می کنند" doesn't fit here and has to be changed to "می کند"

He lives with his family in university او با خانواده اش در دانشگاه زندگی میکند His family and he live in university او و خانواده ش در دانشگاه زندگی میکنند Both English and Persian sentence are same Not difference ....