Your typical galaxy does indeed have much more mass in its dark matter reservoir than it has in its stars. Unfortunately for us observers, stars are the only easily visible part of a galaxy. With the exception of a few nearby galaxies, where we can measure how much of this dark matter is hanging around a galaxy more directly, we have to assume that there’s some extra mass, but it's hard to know exactly how much. In general, there’s something like two to five times as much dark matter surrounding a galaxy as there is matter in stars and gas.
You’re also completely correct that the dark matter component to a galaxy doesn’t seem to collide with anything, and doesn’t feel friction or any kind of aerodynamic drag. As far as we can tell, dark matter only interacts with other kinds of matter (and with itself) through the force of gravity. So with this setup, you would expect two blobs of dark matter to simply pass through each other if they are on a collision course. And yet, we see that galaxies do collide; how is it possible to pull two objects together without any friction?
To get a galactic collision, you need two things. The first is to have two objects moving along a path where they will eventually pass near each other. However, if these two objects are moving too quickly relative to each other, they may just slingshot past one another, never to encounter each other again. This is called a flyby encounter, and happens a lot in clusters of galaxies. Galaxy clusters contain thousands of galaxies, all moving very quickly, and so each galaxy may swing past a number of others, but is moving too quickly to stop and merge with any of them.
So let’s say you have both pieces; your galaxies are on a collision course, and moving slow enough so they won’t go zipping past each other. The speed is critical. The two galaxies need to have some time to influence each other - the longer the galaxies spend near each other, the longer they have to be influenced by the other galaxy. But how do you slow down the galaxy enough to capture it, and eventually merge it into a single galaxy? The slowing is due to a process called dynamical friction. Even if the individual particles which make up a galaxy (which is mostly dark matter and stars) never physically touch each other, they still influence each other through gravity.
Galaxies on a collision course will swing past each other - let’s say they’re moving past each other like two people on escalators going opposite directions (not a bad approximation). The nearest stars in one galaxy pull gravitationally on the nearest stars in the other galaxy, and both sets of stars wind up slowing down as a result. It would be like reaching across the barrier and clasping hands with the person on the escalator going the opposite direction as you; that brief pull between you would pull both of you off balance. Both of you would get pulled towards each other, against the direction of your escalator. (I don’t recommend trying this experiment.) Over time, as every star does this with every other star, and the dark matter particles do this with every other dark matter particle, the stars in both galaxies will come to rest relative to each other. You’ve created a new, single galaxy.
This dynamical friction trick works great for individual galaxies, because both the dark matter and the stars are basically collisionless. Dark matter doesn’t interact with anything except by gravity, and the stars within a galaxy are so far apart that they’re incredibly unlikely to ever collide with another star. But galaxies aren’t uniquely stars and dark matter - there’s also gas: the stuff of nebulae. Gas is different from stars in that it can be compressed easily, and it collides with itself much more easily than the stars do. If you get enough galaxies together (as you do in a cluster), this gas can get pulled out of the galaxy, and heated to such a high temperature that it glows in X-rays.
So what happens if you take a cluster of galaxies, which is made of a huge mess of dark matter, several hundred galaxies made of stars, and a giant cloud of gas, permeating the whole cluster, and fling it at another cluster?
You get the Bullet Cluster, just above. This is one of the most famous clusters because it gave us really solid proof that dark matter was real, observable, and collisionless. The Bullet Cluster is actually two clusters in the early stages of merging together. We can see the two bundles of galaxies, on the left and right of the image. If you trace the amount of mass in each cluster, and then check where the X-ray gas is, you can see that the gas slammed into the gas from the other cluster like a brick wall - the stars and dark matter sailed right on through.