True.
Incorrect. You can download that torrent given the condition that availability of the torrent is more than or equal to 1. And also many times some seeders usually come of that torrent but yes it is not sure, but its incorrect to say that you can't download these torrents.
No you don't need at least one seeder. Say there are 20 pieces and peer no. 1 have 1, 10, 5, 9, 20.
Peer no. 2 have 3, 7, 11, 14, 16, 19.
Peer no. 3 have 2, 4, 6, 8, 13,
Peer no. 4 have 12, 15, 17, 18, 1, 20.
In the above scenario you don't have any seeder but you'll be able to download the files 100% without any problem. Do you disagree???
You are right, I have finished at least a couple of torrents without any seeders. Even quite a few times when there is only 1 seeder, I have seem my torrent getting downloaded from other leechers but no connection at all with the seeder.