I feel a sense of deja vu coming on (the adjacent square issue is a regular) but your point 3 is a worry, since it might seem to suggest that any square adjacent to the Hero falls within the 1 tile attack range.
If the monster is on an adjacent square that is on a tile 2 tiles away, I don't think that 'by tile' attack applies. An 'adjacent' attack still works.
Adjacent attacks would work, but "within 1 tile" attacks would not. Strange but true.