I get about 3 or 4 pairs of Chaffinches in my back garden (I live in a coastal area on the west coast of Ireland). Males are more reddish than the duller females but they have the same white areas on the wings. I agree with you: They tend to mob the ground around the bird table, the bird table itself but not so much the seeds down feeders. I have seen them on them but it's more rare. I have seen them after the sued ball hangers though...
On the subject of the pair although it looks like an even number of males and females, I cannot figure out which one is with who: they very much seem to chase each other off at the moment: Does anybody know if they are "mates" for life of do they change partners every season?