No, there isn't a specific rule for this. The most common is not using indefinite article for professions/occupations.
'Agricultor' is closer for farmer... a 'fazenda' is like the Spanish 'hacienda.' You can be a farmer and not have a fazenda/hacienda (very large plantation farm).
Fazendeira is feminine, "Uma fazendeira". Fazendeiro is masculine, "Um fazendeiro"
Yes, I liked that last time I had to define the gender in English but now it was wrong. Anyway, would be nice, if gender would matter. No to rule but to balance. Yes, I ll report :-)