Containers do have to go to Belize City first and then put on the smaller barges (Caribbean Depot or Mash) to AC. It is possible to clear it through the custom guys on AC.
About the mail, I'm assuming you're talking about a Mailboxes, etc. type place. We used to have one out here on the island a couple years ago. Everything was mailed to a Houston address and then shipped down weekly. We no longer have one but I believe there is still one in Belize City.