Maybe this is what you want:
https://root.cern/doc/v626/classTMultiGraph.html#MG02
If you want to fit each graph separately you can fit them directly (not from the multigraph), as shown also in that page (in “Fit box position”). If you want to retrieve each graph when they are already in the multigraph, you can use GetListOfGraphs, as shown here:
You can look at the integration methods in the Documentation (maybe Integral() is what you want), and to get the fit parameters you can search for examples in this forum, e.g.
https://root-forum.cern.ch/search?q=get%20fit%20parameters