Library - exported functions

Is there a ( simple) way how to check which functions are exported from a particular library?
And how can I find out ( from IDE - during programming)which library a particular command belongs to?

Is there a ( simple) way how to check which functions are exported from a particular library?

Functions are defined in, not exported from, libraries. You have the source code. You can see what functions are defined.

Most libraries define a class. The signatures of a library can then be seen in the .h file.
You must look for the public part.

There exists no tool for in the standard Arduino suite.