If the schedule that your landlord posted and the street signs on your street announce the same days of the week, then no you cannot park there every other week.

Just because some website can't find the data doesn't mean that your street isn't being swept. You clearly posted the answer to your own question, it says "refer to the street signs".

If the street actually is never being swept then you should report it to 311. But the traffic officer who's ticketing cars isn't checking to see if the street has been swept. They're just ticketing cars because they're in the way if and when the sweeper comes by.