Is Hubble's Law used to work out the recession speed of galaxies and stars?
Actually Hubble's derived by measuring the recession speed of galaxies.
Hubble derived his law based on the observation that light from galaxies appeared to be redshifted. When Hubble compared the recession speed of several galaxies to the distance to those galaxies, he discovered a linear trend, showing that recession velocity was directly correlated with distance.
So Hubble's law relies on already knowing the recession speed of a galaxy. The most common way to measure recession speed is using the redshift of light. Astronomers can measure the light curve from a galaxy and depending on how far the light is moved from where it should be, astronomers know how fast the galaxy is moving.