[LONGHAIR]

You have things a bit backward. The spindle has to come off before the axle can come out. Removing the spindle can be a real challenge. There is a specialty tool made to fit a slide hammer, just for this. I wouldn't do it without one.
Nothing, other than the spindle, holds the axle in. It will pull right thru the knuckle.
A small amount of oil may come out of the tube, depending upon how full it is and how level the housing is when jacked up.
If you intend to get into the inner seals, remember that it means tearing both sides apart. The carrier has to come out to access them.
I am not a fan of the pickle-fork to separate the joints. They have a tendency to damage stuff. The simple "big hammer" to the side of the joint works fine.
You need two more specialty tools to reassemble it all. First is a torque wrench, which everyone should have anyway. Second is a socket that is used to torque the upper tapered sleeve during re-assembly.
Beyond that, you need access to a press for replacing the joints in the knuckle, once separated.
All in all, not a simple job.