The real story is that the articles you link to are logically fallacious.
The first hedges its assertions by saying a mailbox is "effectively considered" to be federal property. It cites 18 USC 1705, which it correctly notes "puts your mailbox under Federal jurisdiction." But that's not the same as assuming ownership of it. The piece also says that you "effectively lease" your mailbox to the federal government, which is a somewhat exaggerated way of putting it, but even if we accept it at face value it falls far short of a claim that the mailbox is federal property.
The second concludes that mailbox tampering is a federal offense because "the mailbox belongs to and is controlled by the USPS." There is no evidence offered to support the assertion of ownership, and there is of course an alternative explanation for the fact that mailbox tampering is a federal offense, which is that there are laws such as the aforementioned 18 USC 1705 that prohibit it. These laws, however, say nothing about ownership.
The third is ultimately based on the assertion of a letter carrier who said, "Listen, lady, your friends don’t own these mailboxes. We do." The claim was made in explanation of the prohibition against private individuals putting items into a mailbox. As far as I can see, the article is off the mark in another way: that prohibition has nothing to do with safety and security, but rather with protecting the postal service's revenue: it arises from 18 USC 1725, which explicitly is about avoiding the payment of postage. In any event, it does not establish ownership.
In short, the idea that all mailboxes are federal property is a myth, as implied by the USPS page you link to.
To what extent do property owners have control over their own mailbox?
To a fairly high extent, but they do need to comply with the relevant law. They can't, for example, hang a plastic bottle by the roadside for the purpose of receiving their mail.
Can they deface or place non-mail in their own mailbox?
18 USC 1705 actually prohibits willful or malicious injury, tearing down, or destruction of a mailbox, not defacing. So technically, they could, but a prosecution seems highly unlikely. Under section 1725, placing non-mail in the box is only prohibited to the extent that there is intent to avoid paying postage. That would be difficult to establish for someone putting something in their own mailbox.
Can they tear it down with no intent to replace it?
If they're willing to forego mail delivery, yes. They may be able to arrange to have the mail held for retrieval at the post office. If they do not, their mail will be returned to the sender as undeliverable. This arises from the Domestic Mail Manual, which says (in general) that "customers must provide authorized mail receptacles or door slots" as a condition of city delivery (I could not find a corresponding requirement for rural delivery, but it must exist somewhere). The manual also describes requirements for customer mail receptacles.
