Okeetee corns originated in the area of the Okeetee Hunt Club, which I think was in Northern Florida somewhere (not very sure on that...). They are known for having bright reds and oranges, as well as wide black borders. Some people will use the term Okeetee for any corn snake that shares this look. Others prefer to reserve the term for those corns who can trace their lineage back to corns from the hunt club, and will somewhat jokingly refer to snakes that look like Okeetees but don't originate from that area as Lookatees. Yours doesn't have that Okeetee look, and since you don't know its lineage, I would not call it an Okeetee.
Miami corn snakes originated in the area of Miami, FL, and have red saddles with silver or grey background. Crimsons are a hypo version of Miamis. I think your snake looks much closer to a crimson or Miami than an Okeetee, but without being more sure of its background, my choice would be to just call it a normal.
To answer your specific question, no crimson is not a type of Okeetee.
As for the others, before I read this thread my guesses were:
1 - anery or possibly ghost
2 - definitely amel, possibly motley as well
3 - normal
4 - normal stripe or possibly hypo stripe (eyes are a giveaway it can't be amel, but also the amel stripes I have seen have been more red and less brown in their stripes)
Now that I've read the whole thread, I say just go with what Matthew (Blue Apple Herps) says, because he is one of the most knowledgable people who posts on this forum when it comes to corns.
EDIT: Of course, Matthew was posting while I was and he typed faster, so again I'm just saying "what he said".![]()