Well, I'm pretty sure dimensions in physics are looked upon as something global in a spatial sense. There's no way you can have a couple of dimensions in one place and none elsewhere or one less elsewhere or anything like that. (Except when you're thinking of objects in a space that have different properties, but that's not what I'm talking about here. I was speaking of spatial dimensions we can or might be able to move through. Objects might have dimensional properties one can describe, it doesn't mean the object limits the amount of possible spatial dimensions at all.)
You're right in how dimensions in
theory aren't restricted to physical objects or physical space, but when it comes to real-life applications of the theories involved, we certainly are very much bound to physical space. Unless someday we get those Star Trek 'beam me up Scotty' devices of course.
Hence why 'traveling' through dimensions higher than the 3rd quickly becomes a mostly purely theoretical thing. Especially when it comes to (fictional or not) parallel dimensions or the higher dimensions.
There are still people that think 'time' travel might actually be possible, but they're all talking mostly about wrapping around or curving what is nowadays called spacetime.
Either way much of this talk of dimensions higher than the 3rd is unproven theory, except for abstract usage of dimensions in mathematics which makes sense in that domain.
This means you cannot even define velocity, so a discussion about this doesn't make much sense.
Regardless of dimensions, if there's some kind of movement or motion in whatever dimensional direction that we can observe, sure enough one can also derive a velocity when comparing to say other objects in the same space and dimension which might not move at all. It would be simply defined within a different dimension, but would mean the same thing in practice.
It remains a question whether we can figure out a way to actually detect the higher (spatial) dimensions though, as for example a 1-dimensional being would have incredible difficulties to detect something that's 3-dimensional. I'd say it's perhaps not even possible, or is it?
By the way, I'm not quite following your idea of 'choice related or choice dependent' dimensions here. What exactly does it mean and how much of it has been proven with evidence?
I'm mainly thinking of higher dimensions of physical space in the sense of how the string theory predicts that there are up to 10 maybe even 11 dimensions, all spatial in nature. (Obviously I'm aware that is a theory also.)
