Regarding the USB key: generally, USB keys use one of the FAT family of filesystems; FAT doesn't support security at all, so as soon as you copy the file to it the security information is lost. So for your first question, anyone who has the USB key can read it on any computer from any user account. It is possible to format USB keys using another filesystem (for example, NTFS, which does support security); in that case, if the accounts (in Windows, at least, it must be a domain account or similar, just naming two accounts the same will not do it) do not exist on the target computer, only a user who can ignore filesystem permissions (such as root on *nix or Administrator on Windows) will be able to access the file.
For the second, I'm not 100% sure but I believe it depends on how you copy it; things like FTP and rcp generally don't copy permissions over, so I would assume that the file gets some kind of default permissions for the target directory, or a default built into the copy program, depending on what the copy program does.
For windows, to the best of my knowledge the security descriptor is initially inherited from the target folder; permissions are, again, not persisted across machines. It can be modified after the copy.
In general, except in specific environments that are designed to transfer permissions, I would assume that transferring any file from one computer to another resets the security permissions to a default (generally whatever a new file in that location would receive).