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1. You should consult the Frankfurt "Mietspiegel" (official survey of rental costs) and applicable flat for rent ads to get an idea. As a newbie, especially if you have to find a place quickly (meaning in under three months!), you are likely to have to pay more than average. And if you want a furnished place, far more.
Are you working for a "Central European Bank" (not known to me), or the "European Central Bank", which of course everybody knows (which is right in the center of the city, with few residential areas nearby)?
2. I am not familiar with the Frankfurt area, so cannot comment. But kids at that age learn languages at an amazing speed, so no worries even if you send her to a German kindergarten.
3. Income taxes (and other deductions) depend on many individual factors. But there are online calculators that can give you a rough estimate. I used , entered the abovementioned salary and some assumed parameters that may or may not apply to you, and got a payout of around €3900/month. This is above average (but not rich) for a family of three.

Thanks for taking time to respond.

My bad, yes it's "European Central Bank", thanks for correcting it.

Other than around the main train station in Frankfurt there are no really bad neighborhoods that need to be avoided. One usually concentrates on considering places that have good proximity to work place and/or school/child care - or to public transportation to get there. Sometimes living a bit farther away but close to a U-Bahn or S-Bahn line where one can quickly get to work without changing can be better than living closer but needing to either walk a long way or to need to change trains/buses multiple times.