They can't be, at least not for "perjury", because "under penalty of perjury" has no force unless authorized by a court or, I guess, some specific statute.

The idea that you can stick the words "under penalty of perjury" on a random form to create a legal requirement for truthful answers is one of those Internet legal old-wives-tales, like adding "no copyright intended" to a Youtube upload.

However, if you report that someone else is dead, and they or their family suffer harm as a result, you can probably be sued easily, regardless of whether you use Facebook to make the report, or a carrier pigeon.

"We will suspend your account and you may be liable for civil damages" wasn't severe enough?

I don't get it. There are plenty of legally-enforceable forms online.

The words "under penalty of perjury" have nothing to do with their enforceability.

"Perjury" is lying under oath while testifying in court.

The use on the Facebook page is nonsensical.

Not just while testifying in court. Statutes can also require declarations to be made under penalty of perjury. Valid DMCA notices, for example, must contain one.