How fast are we moving relative to the CMB? The cosmic microwave background radiation should provide kind of a global reference frame, because you can determine your speed relative to it using the redshift.

Is it known how fast we are moving in relation to the CMB? If you subtract the various orbital motions (Earth around the Sun, Sun around the Galaxy), are we standing still in the expanding universe, or traveling in a certain direction?
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 $\sim100\,\mathrm{km}\,\mathrm{s}^{-1}$.