I would not grease the steerer, even a steel one. I've also never heard of a threadless stem seizing on a steerer. As to the slotted cap, yeah, it does look like a good place for water leaks so perhaps a piece of electrical tape over it would be useful.
I also adjust the headsets on my bilkes by rocking them against a locked front brake but some headset makers recommend a tightening torque for the top cap bolt and that works too. Typically its 5 to 20 inch-pounds depending on the manufacturer.