The concentration dependence of the phase stability, half-metallicity, thermal and magnetic properties of Fe2MnxNi1-xSi (0x1) Heusler alloys in two structures, Cu2MnAl (Fm3m) and Hg2TiCu (F43m), were investigated at the ab initio level using density functional theory. The exchange-correlation term was assessed using local spin density (LSDA) and generalized gradient approximation (GGA) along with Hubbard-U (U) corrections. Spin-polarized electronic band structure calculations for Fe2MnxNi1-xSi (0x1) alloys in their Cu2MnAl- and Hg2TiCu-structure have been carried out. These results indicate that the Hg2CuTi-type structure is more stable than the Cu2MnAl-type structure with increasing Mn content, from x=0 to 0.25 using LSDA. No significant differences were observed using LSDA+U over GGA. The full Heusler compounds Fe2MnxNi1-xSi (0x1) are half metals in the Cu2MnAl-type structure for x=0.75 and x=1, and behave like a metal in the CuHg2Ti-type. The minority bands exhibit a band gap of about 0.11 (0.56) eV for Fe2Mn0.75Ni0.25Si using GGA (LSDA+U). Using the GGA scheme, the obtained band energy was smaller than that obtained by using the LSDA+U approach. These results clearly show that the lattice parameter, bulk modulus and total magnetic moment vary quadratically with Mn doping. The main contribution to the total magnetic moment comes from Mn or Fe atoms in B sites in both types of structures. The total magnetic moment of Fe2MnxNi1-xSi (0x1) alloys is typically in the range of 2-3 B in the Cu2MnAl-Type and 3-4 B in Hg2TiCu-Type per formula unit and consists of an average of 2 B per Mn atom and less than 1 B per Fe atom in the Cu2MnAl-Type, and an average of 2 B per Mn atom and around 1 B per Fe atom in the B site Hg2TiCu-Type. Using the quasi-harmonic Debye model, the concentration and temperature effects on the unit cell volume, thermal expansion coefficient, bulk modulus, the Debye temperature and heat capacity, for Fe2MnxNi1-xSi (0x1) Heusler alloys are investigated and analysed.