Can the landlord ask for a late fee payment on a post marked check?

Unfortunately, your rent needed to be received by the landlord on the day it's due or the landlord is fully within his rights to impose a late fee and send a 3 day pay or quit notice. It is your responsibility to work with any third parties that are helping you to insure that your rent is sent sufficiently in advance for it to be timely received.

Depends on the lease language. Most leases require rent to be "received" by the due date and don't say anything about being postmarked. If they accepted the rent you're fine.

If the landlord accepted the rent payment, then he can not use a lack of payment as the basis for eviction. If he refused to accept the payment because it was late and gave you a three day notice for non-payment of rent, a judge might not rule in his favor. Most rental contracts state the rent must be paid by a certain date or there is a penalty [some courts require that penalty to reflect the actual harm done to the landlord]. If on the date the payment was due without penalty the landlord did not have a check which could immediately be cashed, payment was late and you are subject to a penalty.