In a galaxy if the vast majority of the dark matter halo is outside the visible normal matter, how does it pull that normal matter in and allow it to spin faster than it would if there was no dark matter?
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It doesn't. To a first approximation$^\dagger$, only the mass interior to an orbit produces a net inward gravitational acceleration.
The extent of the bulk of visible matter in a galaxy can be seen/measured. What is then observed, is that objects (halo stars, globular clusters, satellite galaxies) orbiting beyond that do so at speeds that suggest there is much more (dark) matter present at these larger radii (but still interior to the orbit) than just the visible matter.
Closer to the centre of a galaxy, it is still the case that orbits are too fast to be explained by just the visible matter interior to those orbits. Although we talk about "dark matter halos", the dark matter density is still inferred to increase with decreasing radius. It is only the ratio of dark to visible matter density that decreases towards the centre.
$\dagger$ It is an approximation that is only strictly true for a spherically symmetric distribution of matter (using Newton's shell theorem). The details are slightly more complex for discs or flattened distributions, but qualitatively similar.
