Does "intimate" = "imply + infer"? Or just "hint at"?
Solution 1:
Intimate 2
verb [with object] 1 State or make known: Mr Hutchison has intimated his decision to retire
verb [with clause] 1.1 Imply or hint: he had already intimated that he might not be able to continue
- ODO
In use, intimating is a hint or statement made intentionally. This precludes inanimate objects from intimating unless the objects represent persons figuratively, as is done in some of the M-W examples you cited.
In the examples you mentioned, the person making the implication is "he", not "she" or "the door". So (1) can work; (2) and (3) don't.