Is that proper to get messages about your work from your lab head at the early dawn? Is that proper to get messages about your work (almost critique no constructive feedback) at the early dawn, I freaked out from my sleepings not the first time to expose that besides the high pressure to get results as soon as possible. I feel my body is exhausted and sick and sometimes crying, is this behavior normal in academia?
It is entirely proper to send emails at whatever time anyone wants to. It is up to the recipient to read them as they see fit.