何て言ったんです is a grammatical structure that indicates what came before it was spoken. If you look it up in the grammar bank you won’t find it, it’s a corruption of 「何々」と言いました or in its plain form「何々」と言った。(The writer has changed the と to a て and put a 何て in front of it, which is kinda like the Japanese word for “kinda”].

But the sentence that comes after also looks like it’s been spoken because of the ［ ］around it.

I think ところ and こと are interchangeable. But こと is shorter (duh!) which means that it’s used in spoken language much more. Often when there are two words that mean the same thing, the shorter is used in spoken language, the longer in written.

なんて is the colloquial version of などと. などと can be broken down to など which means “things like” and と which is a particle to mark a quotation. So, “彼女は僕のことを軟弱だ” is marked as a quotation by と.

The original meaning of ところ is “place.” So, in this case, it would be natural to use ところ because 女々しいところ means a part(= place) of his personality which can be described as 女々しい.　I hope that would make sense.

In this sentence,

彼女は僕のことを軟弱だ、なんて言ったんです。「あなたの女々しいところがもう耐えられない」

when he says なんて言ったんで, which part is the direct object of 言う, is it the sentence that came before, or the sentence that comes after in quotes?

Also, is there some clear difference between ところ　and こと　when used to refer to ‘things of’ a person or a place? Could こと have been used here without a change in meaning?

Thanks in advance.