Akinbo;
The 'force' acts 'inwards', as Newtons. 'Self centric' thinking still pervades all science. We've escaped it a little, in baby steps, but all the time you reject the hierarchical / fractal view of nature you'll be locked in to it, and nature will confound.
3 and 4 need escape from those 'self centric', 'earth centric', barycentric' or even 'galactocentric' viewpoints to rationalise.
Perhaps start from the premise that for understanding nature WE are not important, nor is Earth, nor our sun. There are countless barycentric systems out there, all in relative motion all equivalent, as SR says. Light speed is c locally to all, so is found 'different' if all 'viewed' from one distant rest frame.
Think hard about that. The only logic then is that any valid concept 'speed' is only valid if using the LOCAL background frame as the datum. A car driving at 40mph on Siruis 5 is then NOT doing the 7,340mph we find (a self centric view) but is doing 40mph. Sirius 5 is doing 7,300mph wrt YOU! However it may only be doing 2,000mph wrt it's own local background frame.
ALL speeds are then relative. We stupidly assume we don't have to specify a datum frame for 0. We always must. Only then does it all make sense.
"the CMBR says earth is moving at about 380km/s through space. Can you cast a stone against that?"
It does NOT say that Akinbo! You added the "through space" using a self centric assumption of 'all space'! Read the actual Scott & Smoot (2004 Nobel) analysis.
Earth has a known orbital speed wrt the heliosphere, which has a known speed through the local group, which has a known speed through the cluster, which has a known speed through the supercluster, which has a known speed around the local filament, which has a known speed wrt the 'Hubble Flow'. (Yet even having found and calculated those speeds, now largely confirmed, Smoot couldn't rationalise the pattern without invoking ether and suggesting 'differential expansions'!! It's far simpler.
The fish swims at 3 knots in the river whatever speed it's flowing. It wonders at the intelligence of humans on the bank who insist it's swimming at 6! Wouldn't you?
Best wishes
Peter