Yes. Apply lubricant where the environment permits. And when so doing, there is no need for concern about any loss of self-locking performance. Lubricating the shaft will ease the work involved in any subsequent removal of the nuts.
Are any special tools required?
No. You can use an ordinary commercially available hook wrench.
Can the convex and concave nuts be installed in the reverse order?
Yes. This will not affect the HARDLOCK Bearing Nutfs vibration resistance performance.
Is it necessary to hold the first (lower) nut with another tool when tightening the second (upper) nut?
No. You can tighten each hem separately with a single wrench, as the two nuts will not rotate together due to the construction of the HARDLOCK Bearing Nut. If the first nut is not secured, both nuts may spin around together. In that case, tighten the first nut with a wrench and tighten the second screw with a different tool.
In the case that a gap remains between the convex and concave nuts after tightening, will this cause any problems?
No. There should be no problem. The concave nut controls the amount of torque regardless of the size of any gap. Even if all HARDLOCK Bearing Nuts are tightened with same torque, the gap will vary from one set to another due to slightly different thread accuracy of each shaft and nut.