Both 了s are the perfective aspect particle, marking completed events/results:
They mark that the match is over and the outcome is decided. Functionally they are the same kind of 了.
If you removed them:
Yes, 她赢了我 is grammatical and means “She beat me” (she won against me).
Differences in nuance:
她赢了，我输了。
Puts two parallel clauses side by side. It highlights the contrast between her result and my result.
这次比赛她赢了我。
Focuses more directly on the fact that I was the one she defeated.
Both are correct, but the original parallel structure sounds very natural and balanced in Chinese storytelling.
但是, 可是, and 不过 can all mean “but / however”, and all three are possible here:
Rough differences:
In casual speech, many people use them almost interchangeably in this kind of sentence.
我不生气 = I am not angry.
我一点儿也不生气 = I am not angry at all / not even a little bit angry.
Adding 一点儿也 strengthens the negation. It emphasizes zero degree of anger, which fits the contrast with losing the match:
Literally, 一点儿 means “a little bit”.
But in the pattern:
it usually means “not … at all”. The logic is:
So here:
Outside of negation, 一点儿 can just mean a little:
不 and 没 are both negators, but they’re used differently.
In your sentence, 不生气 describes a current attitude or state (I’m not angry about it), not whether an event of “getting angry” happened or not, so 不生气 is the natural choice.
Yes, you can say:
Differences:
我一点儿也不生气。
Strong emphasis: not at all, not even a bit.
我也不生气。
Means “I’m also not angry”, usually echoing someone else:
e.g. A: 我不生气。
B: 我也不生气。
So 也 alone mostly adds “also”; 一点儿也不 adds strong degree emphasis.
一点儿 (with 儿) and 一点 (without 儿) mean the same thing grammatically.
So you could also see:
All four are fine: