I think you’re right about white “cable” - it feels hollow like a tube and is labeled with “AT&T” and something about being lubricated with silicone (it’s kind of hard to read).

That’s a good idea about the connector. We do not technically need a splitter because we don’t have TV service, but I was going to use it as an informal connector since it’s already there. If the splitter is not actually splitting off into multiple coax cables, can it function as a connector without affecting the signal? Or would it be better to buy a separate connector? Thanks!