I have some c++ written package. Linux, gcc. I can modify compilation process (change Makefile, flags, etc.), but can not change C++ source code.

One runs the package with different parameters, it does a job and exits.

How to count:
1) Number of calls of function with specific name?
2) Number of calls of functions with specific signature?
3) Number of calls of functions where one of the parameters is of specific type i.e. std::string (type is specified by signature)?
4) and extra Number of calls of functions of STL objects, i.e. std::string copy constructor?

(I mean count a number of calls during the run. )

I thought to do it with GDB, but I found it very tough to do (1) and have not found how to do (2)-(4) at all.

All acceptable answers I will write here for humanity.