Hi
Am I not supposed to have Ads?
Am I supposed not to take part in the meeting?
…
If the meaning of the questions (emphasis, tone) changes if I move not before or after supposed,correspondingly?
Is it just my cranky idea that the first (“Am I not supposed…?”) sounds a bit sarcastic, whereas the second is ‘more neutral’?
Hi Tamara
I’d say you’ve got a pretty good grasp of the difference. 
“Am I not supposed to have Ads?”
This means you think you are supposed to have Ads (whatever that is), but apparently you unexpectedly don’t have Ads and you are now questioning that fact. So, yes, this may well be a bit more “crankily asked” than the second sentence. 
“Am I supposed to not take part in the meeting?” (NOTE: My preference would be to put the word not after the word to.)
You are asking a more straightforward (neutral) question here.
Amy
Thank you, Amy.
Especially for that:
Tamara
Hi Tamara
By the way, I’d also say there would be a difference in “degree of crankiness” depending on whether the speaker starts off with a contraction or not. :shiock: For me, using the contraction makes it sound more neutral because it would be the more standard format in spoken English:
“Aren’t I supposed to have Ads?”
Amy
Hi Amy,
I know that amn’t sounds awkward, but I can’t still get used to saying (or writing) Aren’t I…
:shock:
Amn’t doesn’t sound awkward, it only sounds wrong.
But I’m sure the awkwardness of trying to say something as unpronounceable as amn’t is exactly the reason the use of aren’t in such sentences began.
Saying “aren’t I ?” is absolutely standard. 1000% correct for this negative question. 
Amy
Thanks, Amy.
This time I was lucky enough to have corrected myself by myself in a right way. Before 
Yes.
This is just one thing from what I seem to be unable to learn in English.
Sometimes that happens, not rarely.