I think that they are really rude questions. They are a bit like prodding someone on a bruise to see how much it hurts. I mean...
someone said you were a teacher, did you not like it?'
So elderflower never raised being a teacher with this woman, she's heard it and wants to know what the gossip is around it. There are a few possible happy answers e.g. 'no I wasn't a teacher, you got that wrong' 'yes I was a teacher, but then I won the lottery' but the vast majority of answers will be 'yes, I was, I gave it up due to stress/ill health/some other reason that is likely to be personal and thank you SO MUCH for bringing that up.'
'are you not getting anything for your dad for Father's Day then?'
Why would you not get anything for your dad for Father's Day? Either he's dead or you've gone NC due to abuse or some other painful issue, or he left when you were a kid and never came back. Oh the small talk opportunities...
'how much rent do you pay there, then?'
Money. Other people's money, your money, what you earn, what they earn, how much their rent is, how much your shoes cost. I find it very unpleasant as conversation.
'Why do your kids have different dads?'
What can anyone say to that? "Oh because I thought it would be fun! I planned my life that way all along. Divorce is such a lark, I just wanted to do it again. I didn't love the father of my children, so it doesn't hurt particularly that our relationship broke down, and I don't love my kids or feel any desire to protect them, so, yeah, this is a really happy stress-free conversation." Mmm.
Here are some non-rude questions...
'Doing anything this weekend?'
'I love your hair, did you go back to the same salon again?'
'How did 'xyz-thing-you-told-me-about go? I was thinking of you.'
'Your DS scored at football when I went to watch - I took a photo, would you like me to send it to you?'
Because they all relate to something positive. Hence not rude. It's not that everything has to be positive - but I don't just come out and ask people to tell me about their pain - I don't have any right to know about it. I listen and am there for them whenever they want to talk about something that hurts, of course. But only if they want to. (Funnily enough, I am often the one people want to talk to, because I don't gossip)
Admittedly I'm hardly a walking Debretts and can be tactless or irritating in a million ways...