On #1, I'd say you hit the nail on the head. The only other way to take it is that all three are nominated this year, and that her nomination was announced last of the three. But this is farfetched (clearly, nominating a woman for this award is rare—how much more rare would be three at once?!) More likely a reader would think #1 to be a misrendering of one of the other sentences.
On #2 I agree with you. Her nomination was clearly in the past, and one infers that the award was already given as well, and if so, that she probably didn't win it, but you can't be sure of either without further context. One might guess that if she had won, they would have said so; but with only this one sentence out of context, you can't be sure.
In #3 you mistakenly interpreted the infinitive as somehow referring to the future, and deduced that the nomination is not yet known by others. To say simply "she is to be nominated" would imply this, but to say "the third woman to be nominated" implies that she, along with those other two previous woman nominees, is actually known to be nominated. (See discussion at #5 below)
Number 4 is quite similar to #2, but I would say that the "to have been" more strongly conveys the impression that the award has already been given. Still not a certainty, but a bit more likely in #4.
In #5, one might conjecture that she is dead, but I only take the "was" to mean that she was nominated in some prior year (unless the sentence is from an obituary!) There might or might not have been a fourth woman nominated since then. And strictly speaking, if she "was" third, she is and always will be the third, but the use of "was" might only be to confirm that the nomination was in the past, not that she is in the past (dead).
As for your other interpretation of #5, at first I could not see how you came to the conjecture thst she was NOT nominated, when the sentence clearly says that she was. But then I realized that you might have read some conditional (counterfactual) meaning into the apparent construction "was....... to have been nominated". This interpretation is only plausible if the "was" were adjacent to the "to have been nominated". Putting "the third woman" between them makes this reading impossible; "to have been nominated" modifies HER, it does not connect with "was". That is, she was a {woman to have been nominated}, or, more simply, a {woman who was nominated}, that is, a nominated woman.
If she had been expected to be nominated, but was not, one would express it this way:
"HAD SHE BEEN nominated, she WOULD HAVE BEEN only the third woman... [to be nominated]"
"She bit into an apple." This is grammatical and makes sense on its own. In the story of Snow White, biting into a poisoned apple is an important part of the story.
Snow White bit into the fruit, and as she did, fell to the ground in a faint: the effect of the terrible poison left her lifeless instantaneously. (Source)
"She bit off an apple." doesn't make sense without more context. Usually we would say something like "She bit off a piece of apple." To "bite off", a piece needs to be separated from the whole with your teeth. If there was an edible apple tree like the one below, she could bite off an apple (from that tree).
There is an idiom that might help explain it - to bite off more than you can chew. Taken literally, it means that the piece you bit off is so big, it fills your whole mouth making it hard to close your jaw to chew it. I picture something like this
Some more examples:
The dog bit into the man's leg. (Doesn't tell you if the dog has let go, or if the dog has taken a chunk out of the leg.)
The dog bit off the man's nose. (Most or all of the man's nose was separated from his face. Ouch!)
The dog bit the man. (Doesn't tell you where the dog bit the man, or whether it bit anything off, or how severe the bite was.)
Best Answer
"Where she at?" is ungrammatical in standard English. It's missing the copula is:
In some dialects the copula can be deleted, and in those dialects the third sentence is grammatical (but informal). However, this is markedly non-standard English, and if your goal is to speak standard English, you shouldn't talk this way yourself, even informally.
The rules for copula deletion are complex and depend on the dialect in question, so I'm afraid I can't give a set of rules here.
The other question is whether at after where is acceptable. I believe it is, and I cite this Language Log post which argues that it's a feature of standard English. However, some prescriptive grammar authorities would tell you not to use at here. Because this is true, if you were taking a test, I would suggest using the uncontroversial "Where is she?" instead.
Regardless of whether you think at is acceptable, it's certain that many people consider it informal, so I've marked the second sentence above "standard English, informal".