Formulas and expectation values which are need to determine the lowest-order QED corrections (similar to alpha(3)) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the quasi-singular Vinti operator and < r(eN)(-2)) and < r(ee)(-2)> expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived for the bound state properties of the two-electron ions as the function of the nuclear electric charge Q. (C) 2015 Elsevier B.V. All rights reserved.