This is what my experience of these situations generally were, and how we dealt with them
An ultra-orthodox Jew wishes to know if the crew member serving him is having her period.
99% of the ladies I flew with dealt with this in one of two ways.
A) Say no I'm not
or
B) Ask a male colleague to serve them
A monk looking sort if chap (oriental origin, orange robe, sandals, shaved head etc.) won't sit next to "woman" and won't be told what to do by one either. He will get up and down and do as he pleases.
Not experienced this one but had people who have refused to sit down. I took the approach of being persistant. I started by asking and then by telling, becoming more assertive each time. Failing this asking the Captain to do a PA would sometimes work (I was lucky in my airline that 99% of pilots were very supportive in us dealing with awkward passengers). I've seen a lot of sexism onboard and unfortuantely sometimes it's best just to bite the bullet and send the male crew member in who the passenger is more likely to listen to.
Some Asian men believe they can grab/touch any part of our female cabin either to get their attention, demand service or make a point.
The ladies I flew with were very capable and good at dealing with this on their own, a stern but polite word usually seemed to work. At my airline we flew very few routes to this region so this behaviour was rare. One I was working with a new girl and we were both working down the back of an A320, an extremley intoxicated individual thought it was OK to grab and touch her as and when he pleased. She became very upset at this and in the end I had a word, explained that his behaviour was inappropriate and that he had to stop. We then kept her away from him for the remainder of the flight.
The expectation by some passengers that cabin crew will stow their carry on bags and retrieve them at the end of the flight.
As a great senior used to say
"you pack it, you rack it" 
A polite explanation explaining why you can't do it is the only way you can really address it, it's never well received though.
Having said this, I did enjoy meeting and chatting to passengers from all walks of life and I met some very interesting people from all around the world during my time as cabin crew. Despite the thankless task I did very much enjoy the job
