Is there for example some L1 like libration point where the Hill spheres of the Sun and of the Alpha+Beta Centauri meet? And are Lagrange points between stars inside of a binary system, like Alpha and Beta Centauri, more or less stable because they are much more massive than planets?
Lagrange points do exist between stars. In case of single stars, they are too far away from the stars to have any practical effect.
However, in case of the binary stars, the Roche Lobe has its apex located at L1.
In case a star's surface extends beyond the Roche Lobe, it will lose the material outside the Roche Lobe to its companion star through the first Lagrangian point.
Yes, there are Lagrange points between starts, however, most are not stable enough to orbit around them because they are too far away from the stars.