- Qt and Qwt should be compiled with the same compiler to be abi compatible (same major version of said compiler), if linker complains that it cannot find library it might mean that he ignores provided library because it's not abi-compatible. In c++ you cannot just download library and expect it to work unless you're using package manager like vcpkg or conan or msys2. If you're not using package manager, I recomend you to compile qwt instead of installing it, the process is straightforward and compilation only takes about 10-20 minutes.
Canonical gcc way to specify libraries is with -Ldirectory -lname
LIBS += -LC:/dev/qwt/qwt-6.3.0/lib -lqwt
Where should I define, that I want a static binding of qwt libraries?
You should not, if you link to static library it will be linked statically if you link to dynamic library it will be linked dynamically.