Why does a blue star shine blue?
Blue stars shine blue because of the energy that they are
Blue is a higher (more energetic) wavelength of the visible spectrum of electromagnetic radiation.
Blue stars have much more energy associated with them, therefore, the majority of the light that they release is in the higher spectrum...blue light.
Yes, the stars in the sky (including our sun which is itself a star) shine with light that they produce themselves. The starlight is energy produced in the core of the star by a process called nuclear fusion (hydrogen atoms fuse together to form helium atoms + a release of energy) and this energy makes the star shine.