All of those questions are acceptable. Strictly speaking, the possessive pronoun "my" is the grammatically 'correct' option. This is because it is connected to the gerund 'having'. Gerunds function as nouns, so in theory they always need to be preceded by possessive pronouns - 'my having', 'your having', 'our having', and so on. However, the use of the object pronoun 'me' is now very widespread in informal English. It feels natural to the majority of native speakers, and nowadays most English speakers who haven't had a formal education in grammar would consider this to be the correct form. Only the most pedantic of grammarians would correct 'me' to 'my', or mark down a student for saying this. I'm an English language examinations consultant, and the board I work for accepts both forms in grammar tests.

Is there any chance of me having a quiet word with you?