I remember seeing screen shots of a conversation in which an American was quite baffled to learn Aussie Subway restaurants offer carrot, and also that we tend to call the vegetable parts of the sandwich "salad".

Korea karoto ... Idk how it's called in English, maybe "Korean carrot", maybe not

It also accepts "carrots", plural

Also, honestly, a person would likely say, "this sandwich has carrot in it" "ĉi sandviĉo havas karaton en ĝi" since the sandwich is the focus of the communication.

You could say unu karoton for one carrot and iom da karoto for some carrot if you wanted to make the distinction.

Mi havas karoton could be either.

The emphasis is on the last-but-one syllable, yes. That is where I hear it, too.

There is a little emphasis on "sand-" in that recording but it seems to me that the one on "-viĉ-" is slightly stronger, as it should be.

The emphasis is on the penultimate syllable. It should aound like sandviiiiĉo. The emphasis is always always always on the penultimate. For example: Estas, mAnĝas, forgEsas, kAptas. Hope that helps.