- I work morning SHIFTS. My friend works night SHIFTS. ---> "shift" needs to be plural.
- I DO morning SHIFTS. My friend DOES night SHIFTS. ---> again, "shift" needs to plural and also "have" is used for possession, so "do/does" is better because it is used for activities.
- I CHANGED shift with my friend. We talk during the shift change. ---> "change" needs to be past tense because it is already happened. Also this is a little confusing because to change shifts with someone sounds like you were supposed to do a time but he did it instead but you then go on to say you talked during the shift change. So I actually believe you meant to say "I took over from my friend's shift", which would mean that his shift finished and yours began.
- We switch shifts every month. Now I work night SHIFTS and my friend DOES morning SHIFTS. ---> again, "shift" has to be plural and also you missed the the verb "does" from the second part.
- My manager rotates employees’ shifts every month. ---> this one is perfect!