In short, yes. Déjà Vu will randomly collect the last 100 messages in a text channel, pick one at random, and repeat it back into the same channel.
No, collected messages are never saved for later and are deleted immediately after they are gathered.
No.
Déjà Vu will only ever repeat a message in the same channel that the message came from. Messages will never escape a channel or server by Déjà Vu's own hands.
Repeated messages are semi-anonymous. While Déjà Vu only repeats the content of the message and not the poster, someone could see who the original poster is with minimal effort using Discord's built-in search.
Déjà Vu is capable of collecting any message in a text channel. Deleted messages and messages posted by bots are filtered out before a message is selected to be repeated.
You can join the support server or ask Trainmaster2, both linked at the bottom of the homepage.