We addressed possible ambiguities on the properties of neutron stars (NSs) estimated in theoretical sides. First, roles of hyperons inside the NS are discussed through various relativistic mean field (RMF) theories. In particular, the extension of SU(6) spin-flavor symmetry to SU(3) flavor symmetry is shown to give rise to the increase of hyperon threshold density, similarly to the Fock term effects in RMF theories. As a result, about 2.0 solar mass is obtained with the hyperons. Second, the effect by the modified f(R) gravity, which leaves a room for the dark energy in the Einstein equation to he taken into account, is discussed for the NS in a strong magnetic field (ME). Our results show that the modified gravity with the Kaluza-Klein electro-magnetism theory expanded in terms of a length scale parameter may reasonably describe the NS in strong ME, so called magnetar. Even the super-soft equation of state is shown to be revived by the modified f(R) gravity.