Why was the "uma" used this time for a profession?
you may include um/uma, but that's not so common.
Is there any reason why you would?
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).
how would you say "peasant" ?
Why not play the female when using uma fazendeira and the male voice when playing um fazendeiro?
For the greater glory of PC.
The example defines fazendeira as masculine, but it takes uma.
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 :-)