Yes, it has a similar meaning - "at someone's house". But in Hebrew אצל can also mean "in possession of" which I don't think "chez" has.
Sometimes - yes, especially with definite objects, but it's less common. For example, to say "I have the key" you could use "המפתח אצלי". (Never מפתח אצלי, which is meaningless).
Do you mean "definite object" as in an instrument with a definite article like המפתח ? Can we say אצלי מפתח ?
Using "נמצא" is not a replacement for "אצל", the two have different meanings.
The word "נמצא" literally means "is found" or "is located", and it's used many times as a copula when describing a relation of location, for example "I am here" = "אני כאן"/"אני נמצא כאן" or "New York is in America" = "ניו יורק נמצאת באמריקה". On the other hand, "אצל" means "at X's place" or "in possession of".
In this sentence there's indeed a location, so equivalently you can say:
היא נמצאת אצל אבא שלה