good questions and ideas, but in brief the answer is: no. Not on any of them (sorry!)
But I'll go into more detail for you
Spiral arms are actually just 'density waves' Places where the orbits of stars tend to cluster together. Imagine a bunch of circles and elipses, of various shapes. These are stellar orbits, and stars move on them at different speeds too (but still close in speed, and direction). Now, shift all the circles so that the...say left..edges match up. You'll notice that there, it's dark, clustered, dense with lines (orbits)...meaning you'll tend to see lots of stars there. Elsewhere they're spread out, and while you'll see the stars, they won't be a big bright cluster of them.
The stars themselves move much faster than the arms, and thus move through them regularly. I.e. the stars that make up the arms aren't the same stars from year to year (well, longer than a year, but you get the idea). The reason they cluster this way is the spiral arms dense, star packed arms pass through slower moving dust clouds...and cause all sorts of star formation. The stars that form have similar orbits to those in the arm that created them becaue those stars dragged the gases along in their wake.
The stars really close to the core orbit as you'd expect, with orbital speed actually increasing as you head out, since you're enclosing a lot more mass each time you step further out. Then it peaks, and begins to drop (you've exited the big dense central bulge) but instead of gently dropping towards zero (as you'd expect if all/most mass is in the core) it flattens out..meaning that you are encompassing a lot more mass than expected when you step further out...much more than we can account for visually.
Also the 'lines of force' thing you see in books is an illustration only. They don't really exist. The forces are fields, more like blankets than discrete lines. The lines are used to help visualize what's going on, and analyze the forces involved. If you are thinking about the way iron filings group around magnets...forming 'lines of force' that's actually due to how the iron filings become slighly magnetic in the field, and attract other iron filings...creating irregularities in the field (i.e. the main magnet isn't the only magnet!). The magnetic field exists in between, and the lines positions are determined by how the iron was scattered beforehand.
If there was a large clump of DM in the halo, you could detect it by observing the deflection of stars moving past it...but single stars would be hard to use, and you don't really need 'escaping stars' to do it. It's actually being monitored in studies now-adays using the globular star clusters that reside in the halo. Same sorta idea, just a bigger scale.
as for time dilation and frame dragging being a factor...way to small, way to local to have this affect. You'd have to be within only a few thousand miles of a BH to really notice it. And we're talking thousands of light years here.