It's not that it acts as a vowel, so much as it isn't pronounced at all.
A bit of history: where we now use the letter 'h' to mark lenition, we used to use a dot above the lenited consonant. This dot came from an old scribal practice used by monks to mark a letter to be deleted. This was generalised from letters like 'f' which are deleted when lenited to mark lenition in general.
I'm not sure how to explain the grammar exactly. However' the verb "déan (rinne)" is being used as a "briathar cúnta" here. "Dhearmad mé m'fhón" would be a direct translation. "M'fhón" is the direct object and there is no "ar" required. But when "rinne" is used, "m'fhón" is no longer the direct object and we always say "rinne mé dearmad AR rud éigean".