Could you accelerate ferrofluid through a solenoid to provide lift
A ferrofluid is basically tiny iron particles suspended in oil; so your proposal is effectively to use iron particles for reaction mass in a rocket. Yes, that can be done, but specific impulse is proportional to exhaust velocity. It is easier to accelerate very low-mass particles like ions to high velocities in a short distance than to accelerate relatively large particles like iron nanoparticles in the same distance. An accelerator for iron nanoparticles would need to be very long (and heavy) to attain the same exhaust velocity that can be attained with ions in an accelerator a few tens of centimeters long. So, it's a good but impractical idea.