Here is your answers for each sentence:
Number 1
Original: I neither usually wake up at 6 am, nor do I like to wake up at 5 am.
Proper: I don't usually wake up at 6 A.M., nor do I wake up at 5 A.M.
Number 2
Original: We neither wear the same clothes, nor do we eat the same food.
Proper: We don't wear the same clothes, nor do we eat the same food.
Number 3
Original: We don't wear the same clothes or eat the same food.
Proper: We don't wear the same clothes or eat the same food.
Number 4
Original: We don't wear the same clothes nor do we eat the same food.
Proper: We don't wear the same clothes, nor eat the same food.
hehe I asked before the same thing. link[https://ell.stackexchange.com/questions/126696/do-native-speakers-use-double-negatives-in-order-to-mean-positive-situations-rea] FYI please. – Kentaro – 2018-05-27T23:54:40.303