There is one issue with all of the sentences: after the initial "never", following with "ever" is redundant, unnecessary, and is at least bad style if not an error. It's like having "never ever" in a simple sentence.
Removing the "ever", in example 1 we are left with two possible sentences The first is:
Never in my life did I think that I would win a game against you.
... which is just fine as it is.
The second is somewhat complex. The "had" makes past perfect tense, which suggests that there is another "thing" following, but still in the past, that is related to the statement; but that "thing" is missing. It would make sense if something follows, for example
Never in my life had I thought that I would win a game against you, but yesterday I did.
But if you intend to contrast this "never" with the present, you should use present perfect:
Never in my life have I thought that I would win a game against you, but I seem to be in a winning position.
Example 2 makes good use of past perfect; "never had I thought...", and then "until I saw", still in the past.
Using a negative interrogative structure is a (usually spoken) form which communicates that you expect a certain answer, that you have already formed an opinion on the subject.
Do you speak Portuguese?
Have you ever eaten ice cream before?
Is it raining?
These are all neutral questions, I am not communicating an opinion about the answer.
If I say:
Don't you speak Portuguese?
Haven't you eaten ice cream before?
Isn't it raining?
Then you can tell I already have an opinion about those questions. Usually it means that I think the answer is yes.
Sue: "Maria is coming over, but she doesn't speak English so it might be difficult"
Mike: "John, don't you speak Portuguese? You could help her out, right?"
John: "Yes, I do, that'll be no problem?"
Here John knows that Mike thinks that John speaks Portuguese, but wants John to confirm. If Mike said "John, do you speak Portuguese" then John doesn't know that mike thinks the answer is yes.
Another example:
"I'm going out for a walk."
"But isn't it raining?"
Here, isn't it raining? means I think it's raining, am I right?
The other meaning it can have is to express surprise at a piece of information. Similar to the above, but rather than saying "I think the answer is yes" You're saying "It's very surprising that the answer to this question is no!", and it allows the other person to confirm.
So, a bit of a silly example:
"Wow! This is delicious, what is it?"
"Haven't you ever tried ice cream before???"
In this example, I am surprised that he has never tried ice cream, so I am not just asking the question, I am communicating that I will be very surprised if the answer is no.
A very similar structure is like this:
You speak Portuguese, don't you?
You've eaten ice cream before, haven't you?
It's raining, isn't it?
Best Answer
"I have never ..." and "I haven't ever ..." mean the same thing.
"I haven't ..." is not quite the same. Depending on the context, it COULD mean "never", or it could mean that you have not done this in this particular case.
For example, suppose you're boss assigned you to write three versions of a letter to be sent to clients: one in English, one in Spanish, and one in German. Some time later he asks if you've completed the job, and you say, "I haven't written a letter in English." In this context you don't mean that you've NEVER written a letter in English, just that you haven't written a letter in English on this particular subject.