If your rent is due on the 1st, it's due on the 1st. A grace period is just that, a prescribed period of grace extended by the landlord. Do not confuse late rent with late fees. Generally, a grace period is a courtesy that is drafted in a rental agreement or lease so that you won't get dinged with late fees until the end of the grace period. That does not mean that your rent is not due until the end of the grace period. If your agreement states that rent is due on the first of each month, you are late at 12:01 am on the second if it is not paid and, as such, the landlord has the right to seek collection of that debt. He cannot charge you a late fee during the grace period (if you have one in your agreement), but your payment is rightfully his and he has the right to try to collect it. Unless you are habitually late, however, for him to approach you immediately would be a litte bit much as far as I am concerned, but certainly not outside of his rights as a property owner or manager. As far as other reasons to show up at your house goes - with reasonable cause, yes he can show up. You have the "right to quiet enjoyment" of your rented or leased space, so your landlord cannot harrass you (which is admitedly a pretty ambiguous standard), but if the landlord is there for reasonable cause such as to maintain the property, he is within his rights as the owner of the property - especially considering that he also carries a responsibility to maintain safe premises for his tenants (you). He cannot, however, enter your residence at his leasure.
Unless your lease/rental agreement states something to the contrary, he has the right to periodic inspection of the property - including the interior, however, he has an obligation to notice you in advance of such inspection. I think reasonable notice is defined as 24 or 48 hours, but I am honestly not sure about that. There are, however, exception to that. For example, if he stops by the property to repair a sprinkler head in the front yard, but notices something that is reasonable cause for material concern, it is my understanding that he can enter the premises without notice. The term "reasonable" is a legal standard. Accordingly, he cannot let himself into your home and say "we'll I had not seen you all day and I wanted to make sure that somebody was letting the dog out. I do not want a mess on those carpets!" That is not reasonable cause for entry. A couple examples of what I might consider to be reasonable cause would be abandonment, which should be defined in your lease and/or your state or local jurisdition, or seeing water running out of the door - implying that the home is flooded and needs to be addressed immediately. Reasonable notice would not be reasonable in such cases.
Unless your lease/rental agreement states something to the contrary, he has the right to periodic inspection of the property - including the interior, however, he has an obligation to notice you in advance of such inspection. I think reasonable notice is defined as 24 or 48 hours, but I am honestly not sure about that. There are, however, exception to that. For example, if he stops by the property to repair a sprinkler head in the front yard, but notices something that is reasonable cause for material concern, it is my understanding that he can enter the premises without notice. The term "reasonable" is a legal standard. Accordingly, he cannot let himself into your home and say "we'll I had not seen you all day and I wanted to make sure that somebody was letting the dog out. I do not want a mess on those carpets!" That is not reasonable cause for entry. A couple examples of what I might consider to be reasonable cause would be abandonment, which should be defined in your lease and/or your state or local jurisdition, or seeing water running out of the door - implying that the home is flooded and needs to be addressed immediately. Reasonable notice would not be reasonable in such cases.