1. Have you taken your data (and your father's) to GedMatch and/or FTDNA in order to utilize chromosome tools that are not available on Ancestry?

2. For the most part, your matches should be either paternal (in that they match your father) or maternal (in that they don't). However, it is possible to have "false positives", in that there is enough of coincidence in the DNA strands to trigger a match between you and them -- especially if you are looking at Ancestry test results since they look at matching base pairs instead of the way other testing companies/sites do their matches. (And no, it is not just the Very Low matches at Ancestry that this could be -- any of the levels could produce this result).

3. One of the reasons why you can get matches that your parents do not have is that bits that you got from one parent, when lined up right next to bits that you got from the other parent can look like a much longer matching segment to a person (who may or may not be distantly related to you -- as in way back to some common ancestry generations before paper trails).

Does this help?
--Elizabeth