Is it permissible to make an exception by saying "Insha'Allah" (God willing) or "If God wills" in all cases, or are there instances where it is not permissible and certainty is obligatory?

The place for the exception is the future, not the past or the present. The exception applies to something that has not yet occurred. As for what has already happened and materialized, there is no need for an exception. So, one does not say "Insha'Allah" (God willing) when reporting something that has already occurred within oneself, but rather when reporting an action that will happen in the future. Not being decisive about past matters is an innovation (bid'ah), and it is not appropriate to be absolutely certain and definitive about a future matter whose occurrence is unknown.