  In this paper, for any Milnor hypersurface we find the largest dimension of
effective algebraic torus actions on it. The proof of the corresponding theorem
is based on the computation of the automorphism group for any Milnor
hypersurface. We find all generalised Buchstaber-Ray and Ray hypersurfaces that
are toric varieties. We compute the Betti numbers of these hypersurfaces and
describe their integral singular cohomology rings in terms of the cohomology of
the corresponding ambient varieties.
