I thought there might be some kind of hash or signature, but I’m assuming that can be forged along with the main payload?
An attacker might replace a package with a previous one which has a vulnerability. Downgrade attack. Unclear if the apt client will check if version is the expected one after requesting a package.
Of course not, Debian is one of the most robust pieces of software around. They wouldn't do something idiotic like relying on the hash being sent with the payload through the same channel.
I think the idea is that debian distributes the hash themselves through their domain, and mirrors offer the downloads either through http or https. So that you don't need to trust the mirror, you just verify the debian given hash. Only weakness would be a hash collision or a cve like this.
From the short description in the advisory, would seem like the attacker can cause the tool to overwrite the file after signature verification.