How can I prove that OpenGL uses hardware to blend textures for both 2D and 3D textures?
everything ,that every software does, uses a hardware some way or other
blending texture is a thing
OpenGL is a software
so OpenGL uses hardware for blending textures 
Logically proved 
Yes, but does it use graphics card to accelerate the computations for blending?
Yes, if you have the right card and the right drivesr.
i think you can tell by looking to your program. if it runs smooth or at least at reasonable frame rates it definitely IS done in hardware, otherwise you would get an annoying slow result (assuming you’ve implemented some sort of time-based rendering…).
Yup , if you code it to do it
One of the most well known cases is hardware that don´t support multitexturing 
so your glMultiTexCoordXX calls will not work …