It says זאת is a typo, but if one were pointing to "this" item that is grammatically feminine, then of course זאת would be fine. But I'm not a native speaker so I appreciate that AlmogL responded.
I figured that as well, and tryed it, but duo does not accept it. I do not know why.
The word, "זאת" Should really be accepted. I agree. I tried it and it gave me a typo!
would "זות היא שלה" be right as well ?
(format) זאת שלה would work in a specific context (something like "this one is hers, not the other one"). זאת היא שלה could also maybe work (don't take this one, it's hers). But it doesn't come very naturally.
Why isn't it (zot) needed to agree in gender?
זה or זאת would need to match the gender of whatever it is that belongs to her, not match to "her" per se.
Why is זאת שלה wrong?
It wants זה שלה, I didn't know why though
I don't know either. Is the object masculine, maybe?
The default is always masculine, hence זה. In a specific situation where you point to a thing that is feminine, you would use זאת or אלה for plural.