Why do you feel the need to be rude, particularly given that any failure of comprehension is your own?
Let me repeat myself: (a) an email is in writing and (b) you accepted and acknowledged the notice." (Here's a circuit court opinion finding that an email satisfied the statutory requirement for the mailing of a written notice.) You even advertised the unit as available and found a tenant, based upon the notice you received, so even if you convince a court to revisit the question of what constitutes the mailing of a notice you're going to have a dickens of a time convincing a court that you didn't understand that notice had been given, or that you didn't acknowledge and accept the notice with the tenant justifiably relying upon your acceptance of the notice.
If you are admitting that you have no contractual basis to hold her responsible for the $15 fee, then her alleged statement offering to pay the fee would be a non-binding offer to make a gift to you, subject to revocation. Funny -- you want to hold her to statements found in her emails and texts, even as you attempt to disavow your own in order to purport that you didn't receive notice.
Going back to some questions you didn't answer: Your tenant does not appear to agree with you that she agreed to give sixty days notice. Do you have that agreement in writing? Do you have any confirmation from your tenant that she agreed to give sixty days notice to end her periodic tenancy, following the expiration of the initial lease term?
Absent an actual agreement that she provide greater notice, her obligation is to provide notice to end a month-to-month tenancy not less than fifteen days before the end of a rental period -- so absent an agreement, notice on July 19 would have been effective to terminate her lease as of August 12.
Quoting Florida Statutes, Sec. 83.57. Termination of tenancy without specific term.
Quoting Florida Statutes, Sec. 1.01(4). Definitions

