Where is typical location of the projects (sources, object files, etc.)?
I store my projects in $HOME/dev but its entirely up to you.
Where is a typical place for dev environment (Eclipse, QT Creator, etc.)?
I use eclipse and set its workspace pointing to $HOME/dev.
Where is a typical place for the libraries? Are there different places for binaries and for header-only libraries?
Typically libraries are installed to /usr/lib and headers are installed to /usr/include.
Where is a typical place for a various tools for the development (code analyser, git client, etc.)?
Typically these are installed into /usr/bin. I also put tools in $HOME/bin, especially if I made them.
But its more complicated than that. What if you want to develop/test an application with a version of a library that is different to the one that comes with your Linux distribution? Sometimes I will install different library versions in my $HOME/dev folder and compile against those rather than the system version.
Also I run Fedora 21 that comes with GCC 4.9.2, however I have installed GCC 5.1.0 into /opt/gcc-5.1.0 and use that for some things.
A typical project structure for me would be something like:
$HOME/
/dev/
/my-prog/
/src/
/include/
/my-prog.h
/my-prog.cpp
/build-debug/
/src/
/my-prog
/build-release/
/src/
/my-prog
/Makefile