A. Generally if your lease does not spell out the provision of a late fee, you cannot charge it if the tenant pays the rent late. Of course this makes it very important to clearly state it in the lease how much is the late fee.
This brings up the next question - can a landlord charge any amount for a late fee?
The answer is no, it's subject to each state's rules and unfortunately different states have different rules.
But the good news is, Nolo.com has put all the states' basic rent rules in one page here - check it out before signing your first lease as a new landlord.