How fast are we moving relative to the CMB?
Yes, our (i.e. the Sun's) motion in the "global", or comoving, reference frame can be measured accurately from the dipole of the cosmic microwave background. The latest results from the Planck Collaboration et al. (2018) yielded a velocity of
$$369.82\pm0.11\,\mathrm{km}\,\mathrm{s}^{-1}
$$
in the direction
$$
\begin{array}{rcl}
\ell &amp; = &amp; 264.021º\pm0.011º\\
b    &amp; = &amp; 48.253º\pm0.005º
\end{array}
$$
(in Galactic coordinates).

Since Earth orbits the Sun with some $30\,\mathrm{km}\,\mathrm{s}^{-1}$, there's a small, biannual correction to this result. On much larger timescales ($\sim100\,\mathrm{Myr}$) our motion round the Milky Way alters our comoving velocity with the order of $\sim100\,\mathrm{km}\,\mathrm{s}^{-1}$.