I have had things sent there, they will receive packages.
Not sure of mailed packages, but they do accept purchases you make in the parks. If you don't want to lug bags around. You can pick puchases up the next day after 1pm at your gift shop in the Disney resort you are staying at. Only in Disney resorts though.
Yes. https://disneyworld.disney.go.com/guest-services/mail-services/
Thanks! Your answer is awaiting moderation.