Answer 2 is nonsensical; it literally says "we can prove who the sender is because two people have the ability to create the MAC." With a MAC, either party could have created the MACed message; each party knows who created it (you know if you wrote something or not, and if you didn't the other guy did), but they can't prove that to anyone else, nor can they prove they didn't create it after the fact. To do that, they'd have to be able to prove you sent the text over the channel (including some proof it couldn't have been tampered with in transit, say by someone person 2 gave the HMAC key to), but if they could do that they might as well skip the HMAC and say "he sent it, here's proof he sent it."
The one-way channel would mean anything sent over the channel didn't come from person 2. However, you'd have to prove the message you present was in fact sent over the channel, and that no one could send a faked message over the channel (say, after person 2 had given them the HMAC key). If someone sends you something over a channel where it's verifiable that it went over that channel and only they could send something over the channel, and both these things can be proven, that channel again provides non-repudiation without needing the HMAC.
The shared element between these is that two parties can create valid HMACs, and one is trying to prove the other created a particular one. That's like having two people who have identical signature stamps, with one trying to prove the other is the one who stamped something. A MAC by itself can't help with non-repudiation, because either party can create them, leaving you needing to prove that someone is in fact the one who made a particular MAC, which is no easier than showing they made the message in the first place. So answers 1 and 2 are not right; the shared secret is why HMAC can't effectively provide this. (digital signatures, in contrast, don't involve both parties being able to create them, so they're better at providing non-repudiation). (note: non-repudiation isn't actually a technical concept, and courts often accept
s/My Full Name/ as a signature on electronic documents; HMACs might in fact convince someone enough to trust the person claiming you wrote something, even if they don't technically prevent them from forging it).
Answer 3 is indeed wrong; confidentiality isn't needed for non-repudiation. One of the best sources of non-repudiation is a declaration in open court; the non-confidentiality is part of the reason why that provides non-repudiation (i.e. everyone can access the records).
By process of elimination, the answer is 4.