Does my landlord have to accept late rent?

A landlord does not have to accept late rent unless it is within a grace period the landlord agreed to. The landlord may refuse late rent and sue in court to evict you. If the landlord then takes the rent payment or if the landlord had a habit (custom) of taking late rent payments, you may have a defense to an eviction suit for nonpayment of rent.  

Yes, if you are a month-to-month tenant or if your lease allows it. A landlord must give a month-to-month tenant a 10-day written notice to raise the rent for the next month.

If you have a lease, the landlord probably cannot raise the rent during your lease term. Read your lease to find out if it says something different.

If you live in subsidized housing, your rent is usually based on your income and family size. So your rent can generally be raised or lowered if your income or family size changes.

No. Louisiana law does not allow the tenant to withhold rent  when the landlord refuses to make repairs. Your landlord can evict you for nonpayment of rent even though he has not lived up to his duties to repair and maintain your apartment.

Exception: If you  live in subsidized housing, you may have a right to withhold payment. However, you should never withhold rent without first consulting a lawyer.  Improper rent withholding (and it is easy to make a mistake!) can easily lead to your eviction.

If you have a fixed-term lease (for example, a lease that lasts one year or six months), you may have to pay for those months for which the landlord cannot find a tenant to take your place.

If the landlord does not do what he is supposed to do under the lease, the lease may give you the right to cancel. You should talk to a lawyer to find out if you can cancel your lease.