Landlord notice law question

[Mark Stone]

I recently posted a few questions and received a lot of great help and feedback but it left me with one last question I was hoping someone could help me with.

In Florida I am confident I can give my tenant a notice to move out in 15 days since we are on a month to month lease at this point.

I am however unsure of the following:

-Can this be given to him on a weekend, aka today Saturday and therefore the 15th day being Dec 31st

-If I gave it to him tomorrow and the 15th day rolled into January, would he in fact have until the end of January to move out then (going off of a response I received from another member on a different post)

-Anything else I need to be aware of before giving him this notice today, which I would like to do if he doesn't get me rent (which is 12 days late, per usual)

Also, while I am at it does anyone have an opinion on reasonable late fees for late rent. The previous owner of my property wrote the lease we are using and it states, $200 for posting a notice of failure to pay rent, and also a late fee of $5 every day rent is late, with no apparent cap listed. 

Thanks for any help!