Have you learnt about something called 'tag questions'? This is a way of turning a statement into a question by adding a 'tag' at the end. The rule is this: If the statement is grammatically positive, the 'tag' at the end is negative. If the statement is grammatically negative, the 'tag' at the end is positive. Here are some examples of positive statements with negative tags: It's Saturday today, isn't it? You're from Brazil, aren't you? They passed their exams, didn't they? And here are some negative statements with positive tags: You can't speak Chinese, can you? John won't go to the party, will he? They don't need any money, do they? So 'am I?' is the tag for a negative statement. For example: 'I'm not late, am I?' 'I'm not going to make a mistake, am I?' 'I'm not working tomorrow, am I?' Now, here comes the irregular part. We can contract 'is not' to 'isn't', and 'are not' to 'aren't', but we can't contract 'am not' in standard English. That's why we say 'aren't I' when we want to add a tag to a positive statement. Here are some examples. I am on time, aren't I? I'm coming on the trip, aren't I? I'm the best student in the class, aren't I? I hope that makes sense.

Hey Stephanie, aren't I isn't used that often. It's rhetorical e.g. Im good at maths aren't I? It doesn't sound natural, avoid using it! I speak English everyday and never use it! Am I good at maths? is an honest question, that is used all the time! In my mind and in my head are almost identical and either can be used. E.G. In my mind I imagined you to be tall or in my head I imagined you to be tall, they are both right! If you're using it in an essay I'd use mind because it shows that your vocab is more advanced. Hope that helps :)

My personal opinion is that "aren't I" is "I are not", which is horrible grammar. I would say "am I not" because "I am not" is proper grammar. However, "aren't I" seems to have become acceptable in modern times, so use whichever you prefer.

Simple - Do not use it. Very bad English

Aren't I (am I not)? implies that this is a regular state of being or quality that the speaker thinks they possess. A sort of assumption. Am I? Is more of a direct interrogative and the quality or state in question is more in doubt. I hope that I am not confusing you more. It is a subtle difference.