The first three sentences are good.
I would change the fourth sentence to "We are not running a day care here." The expression "day nursery" doesn't sound right in American English.
I would change the fifth sentence to, "Wouldn't you expect someone like me to do such a thing?" if the person were surprised about you doing (or planning to do) the thing, or "Didn't you expect me someone like me to do such a thing?" if the person expressed annoyance or aggravation that you did the thing.