You can still use the floating tap holder with rigid tapping, but obviously using a rigid holder will be less expensive, particularly if a few different size threads are being tapped in the one propgram.
Tap reversing almost instanly is correct.
With regards to tapping paste, it will depend on the material being tapped. There are a few ways around applying tapping compound. A very simple method is to secure a small container of compound out of hams way on the machine table or fixture. When the tapping tool is called to tap the holes, its programmed to dip the tap into the compound. Another method is to place a small push type grease gun filled with tapping compouund, into a holder and set it with a tool lenght offset. Prior to carrying out the tapping operation, the grease gun tool is called and tapping compound is applied to all holes to be tapped.