BTree pseudocode from the slides

BTree.py

# Not actually python, but that's the closest language to the pseudocode dialect the book uses
B-Tree-Search(x, k)
  i = 1
  while i ≤ x.n and k > x.key[i]
       i = i + 1
  if i ≤ x.n and k == x.key[i]
       return (x, i)
  if x.leaf
      return nil
  else Disk-Read(x.c[i])
          return B-Tree-Search(x.c[i], k)

B-Tree-Create(T)
  x = Allocate-Node()
  x.leaf = true
  x.n = 0 
  Disk-Write(x)
  T.root = x

B-Tree-Split-Child(x, i)
  z = Allocate-Node()
  y = x.c[i]
  z.leaf = y.leaf
  z.n = t – 1 
  for j = 1 to t – 1 
       z.key[j] = y.key[j+t]
  if not y.leaf
       for j = 1 to t
            z.c[j] = y.c[j+t]
  y.n =  t – 1 
  for j = x.n + 1 downto i + 1
       x.c[j+1] = x.c[j]
  x.c[i+1] = z
  for j = x.n downto i
       x.key[j+1] = x.key[j]
  x.key[i] = y.key[t]
  x.n = x.n+1
  Disk-Write(y)
  Disk-Write(z)
  Disk-Write(x)

B-Tree-Insert(T, k)
    r = T.root
    if r.n == 2t – 1                   # if the root node is full, split it:
           s = Allocate-Node()         # get a new node
           T.root = s                  # which will be the new root
           s.leaf = false              # which means it’s not a leaf
           s.n = 0                     # it currently has no keys
           s.c[1] = r                    # its lone child is the old root
           B-Tree-SplitChild(s, 1)     # Split the (full) child (old root)
           B-Tree-Insert-NonFull(s, k) # Now we have room to ins
    else B-Tree-Insert-NonFull(r, k)   # Else, we already had room

B-Tree-Insert-NonFull(x, k)
    i = x.n
    if x.leaf
       while i ≥ 1 and k < x.key[i]
            x.key[i+1] = x.key[i]
            i = i – 1
       x.key[i+1] = k
       x.n = x.n + 1
       Disk-Write(x)
    else
      while  i ≥ 1 and k < x.keyi
        i = i – 1 
      i = i + 1 
      Disk-Read(x.c[i])
      if x.c[i].n == 2t – 1 
           B-Tree-Split-Child(x, i, x.c[i])
           if k > x.key[i]
               i = i + 1
      B-Tree-Insert-NonFull(x.c[i], k)

a few questions:

1. Is array, zero based
2. Is the Disk-Write can be no-op if used as in memory data structure?
3. Is assuming that deletion is B-Tree-Search but overwrites existing with nil correct?