2) What's going to happen with a 2 moving grids when apparent horizon was formed? Since I use maximum density tracking mechanism to track the positions of the NSs I want to switch the moving grids off after the formation of the apparent horizon and have only one centre of refinement at the origin.
This behavior is also not controlled by AHFinderDirect, but by CarpetRegrid2. The only way I know to trigger grid changes like you describe is to write your own thorn which inherits from CarpetRegrid2 and changes its variables num_levels[i] as desired. Perhaps someone else can give better advice here.
You do not need to switch off these additional grids, unless the
greatly enlarge the fine grid you are evolving. Carpet combines the
refined regions, and if you have three approximately equal regions,
the combined region will work just fine. Is there a particular reason
you want to switch them off?