Single quotes

My parents referred to me as 'rebel' and 'problem child' when I was a kid.
Can single quote marks set off these words?

When my parents referred to me as a 'problem child,' I often became irritated.
In American punctuation, may I place the comma within the single quotes as I did above?

When I was young, my parents referred to me as 'carrot top.'
In American punctuation, may I place the comma within the single quotes as I did above?

Your 'a,' 'm,' 'q,' and 'r,' need to be written more clearly.
In American punctuation, may I place the comma within the single quotes as I did above? This would be in lieu of italics. Yes or no -- does it work?

Thanks.