That would make it more than a regular NAS file server. It would need to have HTTP/FTP/WebDav services for your data to be accessible outside of your LAN.
No it wouldn't. Assuming it has all the features of the AEBS you can mount it remotely as an AFP or SMB share provided you enable remote access. (not sure if windows can connect to remove SMB shares, I assume so)
Yes it is possible, though not as a ftp, ssh or similar. There are different options, and of course it depends on the architecture of the system. For example, if the time capsule (from now on, TC) is local at our home/ or work, the way to get access to it can be: via AFP for MAC (afp://dir_ip/name_server), via mount_afp for Linux (mount_afp afp://dir_ip/name_server /our_folder), via SMB with windwos (smb://dir_ip/name_server).
If for instance the local time capsule is remote, it is also possible to connect it by using either MAc, Linux or windows. You can contact me alberto@cedint.upm.es, and i can give u further information
as Alb said, it certainly is possible - just ensure that your router/modem is correctly forwarding to the TC and its good to go! i do this every day, unfortuntaely it only supports AFP, i havent tried FTP/SMB.