For you "after the fact" permits my answer is "No". 105.14 describes inspections by affidavit when the project is pre-planned to use an affidavit. Not after the fact.
This seems to be 3 separate questions: Sorry my answer is a little long. IMHO,
1. I would allow Contractor Certification for after the fact work/permit in a very limited and not complex Scope of Work and limited situation. Otherwise, Architect or Engineer Certification.
2. Only if CBO finds Contractor meeting 1&2 family inspector qualifications, and certifying 1&2 family dwelling, or townhouse. Again, very limited Scope of Work.
3. 468.602(2) exempts, ( FS 468 does not apply), those licensed under FS 471, 481, and 489 " ..when performing any services authorized by such license or certificate." However, in this case the Contractor is not performing authorized services, but asking to be found competent and meeting qualification requirements of FS 468. I think it is important to note this is not a blanket statutory exemption, but a FBC specific authorization from the CBO that allows work normally requiring 468 licensure to be performed by this qualified individual. They don't conflict, just 2 separate directives.
No, Section 105.14 is for specific "hazardous or complex" with the affidavit.
Comment - if the concern is to the after the fact work, Section 105.3.1 under action on application. If the BO decides to accept a contractors statement of work done, that would be done under this section.