What is ferrofluid shape in zero gravity? Will it have any kind of spikes? When a magnetic field is applied to a spherical ferrofluid droplet, will it just pull the droplet toward the field as a whole? Or will it do so by creating and pulling many spikes?
As I understood, this is a video of a ferrofluid droplet in space. There are no spikes in it, why?
 A: The typical spiky form of ferrofluids (Rosensweig instability) originates from balancing:

*

*The tendency of magnetic particles to clump into “field lines”. Broadly speaking, it is somewhat energetically favourable for particles to be on top of another magnetic particle as opposed to being as close to the magnet as possible. This effect can also be seen in the classical field-line visualisation using iron filings near a magnet (which does not involve other forces if done on a plane).


*Surface tension, i.e., the tendency of the liquid to keep its surface small. The reason for this is that molecular forces between the liquid particles are stronger than those between the liquid and air (or another gas). Without surface tension, the spikes would become becoming microscopically small and very long.
Gravity does affect the form of ferrofluids, but only to a minor extent; it is not responsible for the typical spiky shape.
If you have a typical ferrofluid demonstration at hand, you can see what happens if you turn it upside down.
For example take this picture of a ferrofluid:

Picture from Gregory F. Maxwell, CC BY-SA 3.0, via Wikimedia Commons.
The effect of gravity can be seen in the spikes on the side not being symmetrical: Their points do not protrude perpendicularly from the blob but lean towards the bottom.
Gravity also causes spikes to be bigger on the side than on the top.
Finally gravity flattens the entire blob – but we lack a comparison to directly see this.
(If you are wondering what causes the spiky structure to disappear very close to the glass, my educated guess is that it’s mostly adhesion.)

As I understood, this is a video of a ferrofluid droplet in space. There are no spikes in it, why?

It’s hard to say what exactly can be seen in this video and what it’s supposed to be demonstrating, but assuming that the black stuff is a ferrofluid, there appears to be no magnet around. If there were a notable magnetic field, the black blob should stick to a wall instead of bouncing around.
