Okay, so there are several meanings of "deprecated"

No, the meaning is always the same: Stop using it.

1. "perl -w" will warn, but it probably won't be removed for awhile (e.g. split to @_).
2. "perl -w" will warn, and it will be removed in the next major release.

There's no such distinction. There's never been a promise that a deprecated feature will be removed in the next version. If you get the warning, it may be gone in the next version, it may be removed later, or it may never be removed.

By the way, deprecated warnings are now issued even without -w.

3. "perl -w" won't warn, but the docs call it "deprecated" or possibly "vaguely deprecated;" who knows what will happen?

A feature won't be removed unless it issued a deprecated warning in the previous version's .0 release, so exists($a[$n]) and delete($a[$n]) won't be removed before 5.18.

who knows what will happen?

If you keep using a deprecated feature, the outlook isn't good.

delete $a[$n] and exists $a[$n] are deprecated(3), whatever that means.

If you read the rest of the sentence, it clearly defines what that means. They are "likely to be removed in a future version of Perl". I don't follow the confusion.