Also be aware that if your camera has zoom or focus adjustments your intrinsics will change. For just focus it might not be significant to matter (depending on your application / accuracy needs).
I’d probably calibrate the camera if you plan on using this for anything serious. It is a bit of a learning curve and requires some up-front effort, but you will get much better results for whatever you do next. (You mention wanting to measure distance etc.) Print a Charuco calibration target (maybe 8-1/2 x 11 size is big enough for your case?) and mount it to something flat (glass works well) and capture 10 or so images from different positions / angles. Once you run the images through the Charuco calibration process you don’t have to worry about it anymore (unless you switch cameras or adjust your optics)
As far as extracting data from the aruco markers, yes you can get much (all?) of what you want with some work, assuming you know the aruco marker size etc. Your accuracy for distance (based on size of the marker, I presume) might not be great. Velocity, rotation, etc. might need to be filtered (expect a lot of “noise” in your measurements)
The aruco marker detection isn’t great at localizing the 4 corner points in my experience. You might be able to refine the results by calling cornerSubpix on the points it returns, but I have always achieved the best results with a double corner (as with the chessboard target). Maybe you can add extra corners to an Aruco marker (to create “chessboard corners”) but I think the aruco detection “needs” a white border around the marker, so I’m not sure if it would work or not.
This feels to me like a “try it out and see what works and what doesn’t” situation to me. You might have to get creative to get what you want out of it. Maybe you’ll end up with a second camera.
Good luck with it!