Do you pay preferential attention to the subtle sensations or the gross?
What is the difference between the two? - could you define the two terms? Whatever is there while observing a specific object should be noted, whatever the definition or texture of it is.
If when noting gross/subtle sensation do you note then move on or continue noting until it passes away?
Sensations are constantly arising and passing away, there is never a need to wait until they pass away as they do that of their own accord all the time. You can move your attention to other sensations than the ones being observed if you wish to do so. (ie. I generally start out with the movement of my abdomen, then depending on what I want to do I move to a different body part, stay there, leave my attention to move freely,... This can be very intuitive or highly regimented, up to you to find out what works best. Whenever my attention wanders I return it to the movement of the abdomen.)
If there are multiple sensations is it better in the beginning when noting to note rapidly moving between sensations (gross or subtle) or to note and only move when the sensation passes away?
What you are trying to achieve is to pay clear, accurate, concise and preferably quick attention to your moment-to-moment experience. You always have the option of moving your attention, changing your object, or changing the focus of your attention (zooming in/zooming out, concentrating on the beginning/end of sensations, observing the in-between stage,...).
Should a beginner at noting note and reflect on arising and passing away only or even at the early stage reflect also on Anatta and Dukha?
It appears to me that the reflection occurs of its own accord, nothing necessary apart from carrying on the noting regardless of what arises. A certain understanding of what is implied by impermanence, no-self and suffering occurs regardless of whether you reflect on it actively or not (ie. the three characteristics are implicit to your actual moment-to-moment experience).