In real-life English, all would be understood. How strictly "correct" they are could be argued. My answer is that third is correct, the second is correct for spoken but not written English, and the first is grammatically correct, but for unaccountable reasons the word "ain't" is considered to be "bad English." The third looks odd in print, because of the repetition of the word "right." Because of the way a native speaker would intone the words, and because of a native listener's ability to process the grammar, it actually sounds OK and the listener might not even notice the strangeness. The problem with #2 is that "aren't" is plural. We CAN say "we are," "are we not," and "aren't we." "I are" is just plain wrong, "are I not" is just plain wrong, and nobody woul every say them. Logically, "aren't" is a contraction of "are I not" so it logically ought to be wrong. But there is no "acceptable" contraction for "am I not." One of the meanings of "ain't" is "am I not," so it is the right tool for the job, but, unfortunately, for mysterious reasons, "ain't" is stigmatized as "bad English." The American Heritage dictionary's usage note for "ain't" says, in part: "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?'" In real life, in speech, I would personally say "I am right, aren't I?" Notice that in theory, "I am right, am I not?" and "Am I not right?" would be good answers, but in reality, as the dictionary says, they sound "stilted."

I understand each sentence you wrote above and all are grammatically correct . The second sentence is "standard " and perhaps the most common. The first sentence is also grammatically correct but "ain't " is often considered to be a nonstandard and informal word however is used in certain dialects regularlt. Aint is Also used in colloquial speech.  "Aint" is a contraction for " am not/ is not/are not/ has not, and have not in the English language vernacular . In certain vernaculars it could have additional meanings. I am American from California , have Southern Relatives and as a Black person - I do use the dialect of AAVE often so it is typical for me to use the word "ain't" I would use the top two. It's my opinion that it is important in language learning to realize that just because something may be non standard, doesn't make it "INCORRECT' especially with the English language. The third sentence is grammatically correct however it is redundant (with the word 'right') so I would prefer to use the top two.

Aren’t I

Only the third is good proper English. I would prefer "Am I not right?" The word "aren't" would be a contraction for "are not", so the second sentence is a grammatical disaster. "ain't" is slang. I don't even know what the word means. It means different things in different places. For example, you might hear "ain't I", in which case it means "am I not". But you also hear "You ain't" in which case it means "you are not". Since the word doesn't actually exist, it is impossible to say it wrong. It's like vinegar - it can't go bad because it already is bad. "aren't I" is

"Am I right or wrong?" is preferable. "i'm right, ain't I" is better than the other two