Each week a prisoner is allowed to send one free letter.
I question whether this is universally true. Perhaps the writer can identify if the website he visited was describing the situation in a particular state or city.
I imagine that jails and prisons in different cities and states each have slightly different rules.
In the Texas prison system, an inmate may send personal "Free" letters paid for by the state only if they are indigent, that is, they have no money in their prison account. I believe these are limited to a fixed number per week or month. And when they do eventually have money deposited in their account, the cost of those letters is subtracted from their account before they can use any of it for personal purposes.
Letters written by inmates with no money in their account for legal matters, to an attorney, or to the Courts, are not limited as to the number which can be sent during any fixed period, but again, they must repay that cost if they receive a deposit in their account.
To prevent reuse of stamps on incoming mail, the prison mail room staff in Texas punches a hole in each stamp.
The use of "FRANK" or "F.R.A.N.K" for a franking privilege is a "urban legend" that circulates around prisons. Those who get away with it are simply lucky that neither the prison mail room staff nor the USPS catches their letter and returns it.
The Auxiliary Marking Club Newsletter
had a few articles on prison and/or jail inmate mail a few years ago. These appeared in Issues No. 13, 14, and 15, all written by the Editor: Tony Wawrukiewicz. Unfortunately these back issues are not available online except to members of the AMC. Scans can probably be obtained form the APRL if one is really interested.