Inheriting month to month tenant

[Elenis Camargo]

Hi BP! We are getting into our third inherited tenant but this one is a little different. The tenants have been month to month for 12 years and do not have a lease at all. I don't mind leaving them month to month because my husband and I plan on moving into the property next summer when we leave New York but I am not sure about a few things. 

1) How long do they have to pay rent before it's considered late? 

2) If they do pay late, can I charge a late fee? If so, how much?

I already know I have to give at least 15 days notice legally for them to move out, although I'd give much more than that considering how long they have lived in the property, but I cannot find information on late payments or late fees. Thanks in advance for the help!