How do galaxies move in space?
Galaxies move though space independently of the orientation of their axis of rotation. That this is true can be appreciated from the fact that their direction through space is relative; that is, in the reference frame of an observer that is passing the galaxy in its plane, it is moving like a frisbee, whereas in the reference frame of an observer who is moving along its axis of rotation, it is moving like an American football:



Galaxies form by accreting gas which often lies in filaments of gas, and this is thought to have a tendency to align their spins with the filaments. Higher-mass galaxies grow by mergers along filaments, which should align their spins perpendicular to the filament. I'm unsure if it has actually been confirmed observationally, but it is seen in simulations (e.g. Krolewski et al. 2019). Thus, a merger between a massive and a low-mass galaxy will have a tendency to make them meet with their spins at right angles of each other. But this alignment is only in a broad, statistical sense, and mergers at all angles do indeed occur.