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]"
Tom is the best expert ...
Assertion of a fact. Where there are agreed criteria then there's no need to hedge an statement.
Djokavic is the current number one male tennis player in the world
When criteria are less certain, or we ourselves are not sure of our facts, or we wish to be modest by appearing to be uncertain of our facts we may use I think
I think Djokavic is the best male tennis played of all time
I think that the population of the UK is 50 million (actually 65 million)
This formulation implies that we are open to correction and discussion
Adding would softens this further, emphasises that we are uncertain
I would think that the population of the UK is greater than 50 million
The I would have thought formulation is normally used in a context where some information has recently been given. Depending upon the context it may imply that we are actually contradicting the information, or that we are expressing surprised acceptance.
I think Tendulakar is the best batsman of all time
I would have thought Bradman had a better record
that was disagreeing, suggesting that by some criteria Bradman is better
The current UK population is 65 million
Oh, I would have thought it was only 50 million
but now I've changed my opinion (this implied but not said)
that was agreeing, I thought it was 50 million, but I accept your statement of 60 million is correct. We could just say
Oh, I thought it was only 50 million
With pretty much the same meaning, the slight difference being that the second case implies it was actively in my mind, whereas the would form could imply that I hadn't really formed a solid opinion until now, but I would probably have guessed 50 million.
As your comment indicates we are indeed into shades of meaning and idioms. In these cases the tone of voice will often differentiate the meaning.
I would have thought Bradman had a better record
Would probably said with a questioning or challenging tone and raised eyebrow.
Best Answer
"Wouldn't have been necessary" is quite correct and a normal-sounding everyday phrase.
"Would have been unnecessary" sounds a little more formal and forceful, perhaps even less polite in some context.