Can AES decrypt with a wrong key?
AES-128 uses the full set $\{0, 1\}^{128}$ as keyspace, and for each key the blockcipher is defined for each input block in $\{0, 1\}^{128}$. The same goes for AES-256, but it uses a 256-bit keyspace (but still a 128-bit block).

So the answer to 1 is yes.

For 2, we have this equation:

$$AES_K(AES_K^{-1}(x)) = x$$

We can decrypt both sides:

$$AES_K^{-1}(AES_K(AES_K^{-1}(x))) = AES_K^{-1}(x)$$

Because we know that $AES_K^{-1}(AES_K(a)) = a\:$ by the definition of the inverse we can cancel out an encryption/decryption cycle on the left hand side:

$$AES_K^{-1}(x) = AES_K^{-1}(x)$$

So it's true.