The moon is illuminated by the sun. It is not a source of light itself although it may be used as a source for moonlight photos. For all practical purposes the brightness of the sun's illumination does not change. The phases of the moon are just a result of the sun's Light hitting at different angles. The illuminated part is just as brightly illuminated as when the moon is full.
Since the intensity of the sunlight on the moon is constant, the exposure is constant.

There are three factors affecting the exposure; ISO, shutter speed and aperture. The Loony Eleven Rule gives on possible combination that will be correct in order to show the features on the moon's surface. However, other combinations are also possible for example, instead of using f/11 & 1/100 s at an ISO of 100, you could equally well use f/8 & 1/200 with the same ISO. This is the concept of reciprocity. There are of course many other combinations of shutter speed and aperture that could be used but it is rather pointless to list them all.

If you are really fussy about an accurate white balance, and I don't see this as an issue use 5800 K, the temperature of the sun's surface. Note that this is not the Daylight white balance on your camera since it is calculated using a combination of the sunlight and the blue light from the sky.

As far freezing the relative motion of the moon as the relative motion you do not have to worry unless your exposure is longer than one second. Using a fast shutter speed to prevent motion blur of the moon is like doing the same to freeze the motion of a slug crawling along a leaf. Far more relevant is having a fast enough shutter speed to prevent vibration on the tripod. If that concerns you lock the mirror up, use a shutter release and hang a weight from the centre post of the tripod.

I hope this rather long explanation answers all your questions

RRS and Kirk are very good, but also very expensive. I use an Arca BBH-200 ball head for my larger tripods, a Sirui travel tripod with C-10X ball head, and a Kirk MPA-1 swivel tilt monopod head. I use various Manfrotto and Neewer Arca plates, and generic Arca L-brackets. My gimbal head also takes Arca.

Arca QR systems are particularly useful for L-brackets and gimbal heads. The L-bracket allows mounting of a camera in landscape or portrait orientation. A long Arca plate on a gimbal allows positioning of the lens for balance.

The drawback of Arca is that most Arca systems are not as quick because they require screwing and unscrewing the clamp (a lot if you have stops installed on the plates).

The other issue is that the swivel tilt monopod head doesn't work with the L-bracket. For monopod use, I prefer the Manfrotto QR; it's quicker to mount and release. But it doesn't support portrait orientation. So I use an Arca adapter attached to a Manfrotto QR plate, and then mount the L-bracket on the Arca adapter; this all mounts on a Manfrotto swivel tilt head.