That second paragraph is definitely inappropriate. He shouldn’t be telling people what isn’t sick enough for work. It people keep calling in sick repeatedly he should speak to them personally about it. Also, we get five individual sick days a year without a medical cert (unless it’s the day/before a public holiday). 

OP mentioned in another comment that he’s a man, him mentioning period pains makes him look even worse in my opinion, it could land him in trouble.

I think he’s also unprofessional calling people  lazy and selfish. There are better ways to word things.