Yeah. Think of Beta emission as the decomposition of a neutron into a proton and an electron. The electron is then shot out of the atom. Per the laws of conservation of mass/charge, the nuclear mass of the atom doesn't change, and the negative charge of the electron that was shot out is balanced by the formation of a proton in the nucleus. (While the mass isn't exactly conserved, that's just nitpicking.
) The reverse happens in electron capture "deacy". During electron capture, a proton in the nucleus combines with a "captured" electron to create a neutron, thus decreasing the atomic number by one.
As for the stability, go into the links section and take a look at Theodore Gray's Periodic Table Table. If you click on the Technetium tile, it will contain a link to a VERY detailed and solid explanation about the "Sea of Stability" in regards to proton/neutron ratios.