1. Bob can decrypt the message by multiplying times the inverse of the secret matrix Alice gave him.
2. Eve would be able to decrypt the message without the inverse matrix. There are nine unknown values in the inverse matrix, and conveniently she has nine inputs corresponding to nine outputs. Since matrix multiplication is a linear operation, she would be able to get nine equations containing the nine unknowns and solve for them.
3. Using Matlab and my extensive knowledge of the English alphabet, the decrypted message would be BWE.