Is there a difference in terms of security between
An encrypted stream of bits obtained by encrypting a plaintext concatenated with it's signature
$ C = E_k(plaintext||\sigma)$
where $E$ is a symmetric or asymmetric encryption function, II is a concatenation operator and
$\sigma=h(plaintext)^k$
where $h$ is a secure MAC (the key is assumed to be the same).
A bit stream obtained by concatenating a ciphertext and the signature over the its corresponding plaintext
$C=E_k(plaintext)||\sigma$
where
$\sigma=h(plaintext)^k$
A stream obtained by encrypting the ciphertext of the plaintext concatenated with the signature over the respective ciphertext
$C=E_k(E_k(plaintext)||\sigma)$
where
$\sigma=h(E_k(plaintext))^k$
Also, is there any risk due to using the same key for both encrypting and signing? I don't refer to the cases that do not involve recovering the key through other means other than passive or active attacks.
