Can a shift cipher attain perfect secrecy?
The Caesar cipher (aka Shift cipher) has, as you said, a key space of size 26. To achieve perfect secrecy, it thus can have at most 26 plaintexts and ciphertexts. With a message space of one character (and every key only used once), it would fit the definition of perfect secrecy.

For the usual use with messages longer than one character, or multiple messages with the same key, none of the given options fit (other than the "None" option).