From my understanding, the Hubble constant $H_0$ calculates from observed redshifts $z$ of distant galaxys against their proper distance $D$. The current value appears to be 67.80(77) ${\frac{km}{s}}Mpc^{-1}$.
Does this mean that at a distant of 1 Mpc space expands with a rate of 67.80(77) ${\frac{km}{s}}$? Breaking it down to a more comprehensible scale => $H_0 = 2.197 \times 10^{-18} {\frac{m}{s}} m^{-1}$. So every ~15 minutes ($\approx$ 1000 sec) one meter expands by the size of one proton (assuming $r_{proton} \approx$ 1 fm)
Is this a right image that I got out of it?
Bonus question:
Calculating the Hubble constant via the redshift, I assume one only wants those velocity contributions due to the expansion of the universe, and not those from the real movement of the galaxies within in cluster or so. How do you account for that?