In fact, it all depends on what you do with your smartphone. In general, it will not deteriorate from shaking. However, there is a risk, firstly, of dropping it, and secondly, while running, a person has a habit of sweating, so in theory the smartphone may suffer from moisture. Nevertheless, both of these reasons depend solely on the format of using the phone and, one way or another, you can protect against them. Run, just think about these things.
I don't think so. It is unlikely that there can be damage to something. The only thing that in theory can be - the accelerometer wears out. (http://geek-nose.com/akselerometr-v-telefone-chto-eto-princip-raboty-foto/) Although, probably, it is designed for this.
Because my answer: no.