Ok, trying to help here, one by one.
1 - How does 'Caçadores de diabo' sound as an unoffficial, general self-designation for Brazilian monster hunters, mostly members of military or police special tactical units like CORE, BOPE, GRUMEC, etc.?
Sounds good, but it's literally 'Devil Hunters'. For Demon Hunters it's more acurate the term:
Caçadores de Demônios.
Caça-Demônios can also be used, it's a little more informal. You can switch Demônios (Demons) for Monstros (Monsters) on each one; so,
Caçadores de monstros ou
Caça-monstros.
2 - Does anyone know if Brazil might have Caçadores units in their military, which could mean that monster hunters not in those units would not use the term to describe their work?
Yes. Brazil has
Caçadores units, like so:
https://pt.wikipedia.org/wiki/Ca%C3%A7ador_(militar). In modern Brazilian military, this term came to be denominated "pressure combat" in precision shooters of the Army; which must always be in pairs and are responsible for harassing enemy troops. So, you can look for a substitute name, if you like; OR use
Caçador despite all this as a cover up name for covert ops, perhaps.
3 - And what words might Brazilians use to refer to a commando, in a general sense, regardless of his specific unit or whether he's a soldier or police officer?
We use
Comando (
https://pt.wikipedia.org/wiki/Comandos), really.
Other than that, I'd call it
Forças Especiais, or Special Forces. Some kind of synonym like that.
4 - What are some good terms for intelligence analysts, investigators and the equivalent of Special Agents in the US intelligence and law enforcement community?
Intelligence analyst is
Analista de Inteligência; Investigator is
Investigador. Plural is
Analistas de Inteligência and
Investigadores. Both terms are widly used by brazillian officers. You can also use
Detetive / Detetives (detective).
5 - Oh! And, obviously, what kind of terms might Brazilians use for 'monsters', magicians, the occult in general, etc.?
Monstro (monster),
mago (wizard),
mágico (magician),
feiticeiro (Sorceror),
bruxo (warlock),
bruxa (witch),
sobrenatural (supernatural),
fantasma (ghost),
vampiro (vampire),
estranho (weird/strange),
lobisomem (werewolf)... In general terms,
monstro or
criatura can be used.
Bicho can be used as well... it means animal, but in a creature kind of way, undefined animal.