If the files are stored on tape in the back end they can take up to a few days to recall. Most cold storage solutions use a combination of MAID and LTO Tape, it’s the reason they are so cheap compared to anything else. If that’s not a problem for you and you have a very reliable transmission medium then it will work just fine.
It doesn’t. The data that has been backed up is kept locally in a SQLite database so it knows what files have been backed up.
You can use any backend that is supported by Duplicati. Personally for my remote backups I use an offsite FreeNAS box running FTP over SSH. For the money that you spend on cloud storage you can just set this up.