Conditions for Perfect Secrecy with the Vigenere Cipher
As far as I can tell, your original reasoning is correct.  To obtain perfect secrecy with a Vigenère cipher, the key must not repeat.  The key does not repeat whenever it is at least as long as the message, so option 2 is clearly a sufficient (and indeed necessary) condition for perfect secrecy, at least as far as only key length is considered.  Options 3 and 4 are subsets of option 2, so if choice 2 is correct, then they must be correct as well.  Thus, the correct answer (unless this is a trick question) should be (2, 3, 4).

Note, however, that there are conditions on the perfect secrecy of a Vigenère cipher other than key length.  In particular, to obtain perfect secrecy with a Vigenère cipher:


the key must be at least as long as the message,
each of the key letters must be selected independently and uniformly at random from the entire ciphertext alphabet, and
the same key must not be used for more than one message.


The options in the question you quote make no mention of the second and third conditions, so arguably, none of them is sufficient to guarantee perfect secrecy.  While I would consider this to be a rather nasty trick to play on the test-taker (especially given that such an argument would seem to contradict the "correct" answer to the other question you quote), technically this would be a valid answer (and arguably the valid answer) to the question.



Ps. One possible interpretation, which just occurred to me, is that your course might be using a definition of perfect secrecy which is violated if the length of the message is revealed to the attacker (and is not the same for all valid messages).  This is actually a reasonable definition to adopt: if the attacker knows in advance e.g. that your message is either yes or no, then simply learning the length of the message will tell them which one it is.

Since Vigenère encryption does reveal the message length, this would rule out option 2, leaving only options 3 and 4 (where revealing the message length gives no information to the attacker, since all valid messages have the same length) as correct answers.