1.10)

Solving the first by substitution:

(A 1 10)
(A 0 (A 1 9))
(A 0 (A 0 (A 1 8)
(A 0 (A 0 (A 0 (A 1 7))))
...
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 1))))))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 2)))))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 4))))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 8)))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 16))))))
(A 0 (A 0 (A 0 (A 0 (A 0 32)))))
(A 0 (A 0 (A 0 (A 0 64))))
(A 0 (A 0 (A 0 128)))
(A 0 (A 0 256))
(A 0 512)
1024

The second:

(A 2 4)
(A 1 (A 2 3))
(A 1 (A 1 (A 2 2)))
(A 1 (A 1 (A 1 (A 2 1))))
(A 1 (A 1 (A 1 2)))
(A 1 (A 1 (A 0 (A 1 1))))
(A 1 (A 1 (A 0 2)))
(A 1 (A 1 4))
(A 1 (A 0 (A 1 3)))
(A 1 (A 0 (A 0 (A 1 2))))
(A 1 (A 0 (A 0 (A 0 (A 1 1)))))
(A 1 (A 0 (A 0 (A 0 2))))
(A 1 (A 0 (A 0 4)))
(A 1 (A 0 8))
(A 1 8)
(A 0 (A 1 7))
...
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 1))))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 2)))))))
...
256

The third:

(A 3 3)
(A 2 (A 3 2))
(A 2 (A 2 (A 3 1)))
(A 2 (A 2 2))
(A 2 (A 1 (A 2 1)))
(A 2 (A 1 2))
(A 2 (A 0 (A 1 1)))
(A 2 (A 0 2))
(A 2 4)
(A 1 (A 2 3))
(A 1 (A 1 (A 2 2)))
(A 1 (A 1 (A 1 (A 2 1))))
(A 1 (A 1 (A 1 2)))
(A 1 (A 1 (A 0 (A 1 1))))
(A 1 (A 1 (A 0 2)))
(A 1 (A 1 4))
(A 1 (A 0 (A 1 3)))
(A 1 (A 0 (A 0 (A 1 2))))
...
(A 1 (A 0 (A 0 4)))
(A 1 16)
(A 0 (A 1 15))
(A 0 (A 0 (A 1 14)))
...
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 1 1))))))))))))))))
(A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 (A 0 2)))))))))))))))
...
(A 0 (A 0 (A 0 (A 0 (A 0 2048)))))
                    4096
               8192
          16384
     32768
65536

The functions defined give:

f n = 2n
g n = (A 1 n) = 2 * (A 1 n-1) = 2 ^ n
h n = (A 2 n) = (A 1 (A 2 n-1)) = (A 1 (A 1 ... (A 2 1))) = (2 ^ (2 ^ (2 ^ ... (2))...)) for N 2s
uh... actually this is wrong.

(A 2 1)
2

(A 2 2)
(A 1 (A 2 1))
4