Yes, that is roughly what System Modeler does.
If there are many options in different phases, how does System Modeler determine to choose which method? I don't see any option to allow users to choose the method, so System Modeler must do this automatically. Where could I find the detailed info about the solving DAE process in the system modeler?
This question is far too broad to answer.
If you have a specific question, something you would like to with System Modeler, or a suggestion about the product, I might be able to help you better.