Twitter – Why do the Twitter mentions dissapear

Downloading your Twitter archive allows you to browse a snapshot of your Twitter information, starting with your first Tweet. Behind link there is Twitter help page which explains how in 5 steps, step by step, request Twitter to create downloadable .zip archive of (quote) "your information from first twit". Since it might take time, they promise send you a link by email after task is finished.

If you delete a tweet it disappears for ever (although in some cases they may appear in Twitter search for a little while after)

Twitter and any clients using the streaming API will remove the tweet from a users stream almost immediately. Other clients using the REST API will remove the tweet once the timeline is refreshed.

I'm not 100% sure on what would happen mid-reply but I would have thought the reply will be sent successfully as the id of the now deleted tweet will have already been attached to the new tweet. I guess it would depend on how each client handled incoming and outgoing tweets. In any case the worst thing that would happen would be an error message being to displayed to the user.

Deleted tweets will disappear from a conversation chain.

I'm not sure if deleting tweets is frowned upon but if the information you have posted is incorrect or you no longer want to tweet it then it's entirely up to you as to whether you delete the tweet or not.