Microwave expansion of a plasma is certainly a promising process by which to obtain a large-diameter plasma profile; however, it generates instability regions and local inhomogeneities. The purpose of this work is to study the wave-propagation conditions and plasma-expansion profile in a pure argon discharge and in argon-methane mixture. Spatially resolved plasma parameters are measured using an array of electrostatic probes (simple and double) moving along the discharge axis. This device gives radial and axial measurements which are correlated to the spatially resolved Ar(420 nm) emission line intensity. We show that, as expected, the wave-propagation conditions are satisfied within the luminous part of the discharge. In this region the electron energy distribution function (EEDF) can be roughly approximated by using a Maxwell distribution function of low temperature (about 1000 K). The absorbed microwave power is mainly transferred to electrons as potential energy. Instabilities appear at the edge of this luminous region, where the wave-propagation conditions are not satisfied. In this region the EEDF is strongly disturbed and cannot be approximated using a Maxwell distribution function. The microwave incident power is mainly reflected, so the potential energy of electrons decreases strongly. Nevertheless, the kinetic energy of electrons increases because of stochastic electron heating due to strong inhomogeneities in the charged particle density producing local electrical fields. When methane is mixed with argon, the energy necessary to maintain an electron free in the plasma increases with increasing frequency of inelastic collisions. Consequently, the plasma expansion length decreases with increasing percentage of methane added to argon.