1.

# Helper method for RoG
RNeighs:=proc(k,n) local i,s,t:
  s:={};
  for i from 1 to n do
    t:=[0,i]:
    s:={op(s),t}:
    t:=[0,-i]:
    s:={op(s),t}:
  od:
  for i from 1 to k do
    t:=[i,0]:
    s:={op(s),t}:
    t:=[-i,0]:
    s:={op(s),t}:
  od:
  s:
end:


RoG:=proc(k,n) local V,E,i,j,T1,v,Neighs,Moves,m,pt:
  V:=[seq(seq(seq([i,j],j=1..n),i=1..k))]:
  for i from 1 to nops(V) do
    T1[V[i]]:=i:
  od:
  E:=[]:
  for i from 1 to nops(V) do
    pt:=V[i]:
    Moves:=RNeighs(k,n):
    Neighs:={seq(pt+m,m in Moves)}:
    Neighs:=Neighs intersect convert(V,set):
    E:=[op(E),{seq(T1[v],v in Neighs)}]:
  od:
  E,V:
end:


SAWnu(RoG(3,n)) = 2,6,96,3132,252240,36307440, ...
No


2. 

NuW([40,40],{[1,0],[0,1],[1,1],[2,2]}) = 2382564832244243056285491057263

NuGW([40,40],{[1,0],[0,1],[1,1],[2,2]}) = 89322096703094945357683861273

NuW([n,n,n],{[1,0,0],[0,1,0],[0,0,1],[1,1,1]}) for n = 1,..,20 = {7, 115, 2371, 54091, 1307377, 32803219, 844910395, 22188235867, 591446519797, 15953338537885, 434479441772845, 11927609772412075, 329653844941016785, 9163407745486783435, 255982736410338609931, 7181987671728091545787, 202271071826031620236525, 5715984422606794841997001, 162016571360163769411597081, 4604748196249289767697705221}

NuGW([n,n,n],{[1,0,0],[0,1,0],[0,0,1],[1,1,1]}) for n = 1,..,20 = {2, 10, 88, 1043, 14778, 236001, 4107925, 76314975, 1491934038, 30389576308, 640286048416, 13877540824735, 308102204007536, 6983346070924707, 161156356282624227, 3778249609096250059, 89826197363219012470, 2162338803354415120414, 52637415804379149938876, 1294313658632145337351381}