With regard to #2, "am I not" is correct. "Am not I" is incorrect.
With regard to #1, this is a matter of opinion and a topic of debate!
The short answer is: as long as you are in an English class, say "am I not?" but as soon as you get out into the real world, say "aren't I?"
In real life, almost everyone says "aren't I," including well-educated careful speakers.
"Am I not" is excessively correct, stilted, and pedantic.
The problem is that there is no accepted contraction in English for "am I not."
The American Heritage Dictionary's excellent usage note says:
"The stigmatization of 'ain't' leaves us with no happy alternative for use in first-person questions. The widely used 'aren't I?,' though irregular, was found acceptable for use in speech by a majority of the Usage Panel as long ago as 1964, but in writing there is no acceptable substitute for the stilted 'am I not?'"
#3 is correct.
#4 is incorrect.