The market has long since closed for the day, and there doesn't seem to be any patrols.
Should be "don't"
That sentence is fine because making it "there don't seem to be" is not right. "Doesn't" being there is perfectly fine
No, it's not. The subject is patrols (plural) so it's don't not doesn't (if the subject were patrol (singular) then doesn't would be correct).
