Legally you only have to make your rent payments to the person/entity listed on your lease.  If you are being asked to make them to someone else, get that request in writing from the Landlord.  Her written statement should cover not only future payments made to the daughter but should also include a statement that any prior payments made to her were for rent as well .Under NY law a Landlord is not required to provide appliances unless the lease states otherwise.  However, if you purchased your own than you have the right to take them with you upon expiration of the lease.  I would also get the Landlord to acknowledge in writing the fact that you provided the refrigerator and so it is your personal property.  This will prevent any confusion when you are vacating the premises (and be sure to keep the purchase receipt).As for the son's harassing you about late charges I'm not certain of the facts here.  You didn't make the details clear.  If there is a grace period in the lease (there should be), then notify the LL of that and tell her to stop having her son harrass you.  If he doesn't, you can pursue the matter legally.  Landlord-Tenant law in NY is heavily regulated and tenant's rights are strictly enforced.By the way, when your lease is up you may want to consider getting out of there.