On the bright side, the changes to the kilogram might begin to address the obesity crisis.
Not vibrations of the atoms themselves. The second is defined in terms of the period of the radiation corresponding to a particular hyperfine transition of the Cesium atom.
Basically, as more and more precise measurements of the energy levels of electrons in atoms were made in the 1920s, 30s, and 40s, physicists kept finding that energy levels that were thought to be degenerate (i.e., multiple states with the same energy) were actually split into multiple, closely spaced levels. The original quantum model was the non-relativistic Schrodinger equation as applied to the atom. Then it was found that electron energy levels that were degenerate in that model were actually split into multiple levels because of the effects of electron spin and certain relativistic corrections; this splitting was called "fine structure". Then it was found that there was even further splitting, of energy levels that were degenerate in the fine structure model, due to interactions between the electron and the nucleus; this further splitting was called "hyperfine structure".
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Not really. Detecting the voltage or current differences that you need for detecting an electron spin, that's a very different thing than doing the quantitative measures you need to redefine the ampere.
For example for measuring a single electron, you can use avalanche effects, which are relatively simple to realize, but would not be suitable for the quantitative approach you need to define an SI unit.
I'm not very well-informed regard quantum computing, but the problem with it seems to be more in realm of keeping the quantum states stable and controlled, and less on the measurement side.