Actually, this isn’t accurate. They don’t believe the Church needed to be restored because it became corrupted. They believe it became corrupted because it lost “priesthood authority” upon the death of the last Apostle. They deny apostolic succession, not believing that it was passed down to the successor of Peter and the other bishops.
Not true. As the OP said, the Didache was written very early on while at least some of the Apostles were living. Their claim is that authority (and truth) only left the Church when the Apostles were no longer around. I think this is a good question. The bottom line is that nothing they claim about the “Great Apostasy” has any evidence to support it.
Try to imagine that the Church that Christ started, in which He promised to remain until the end of time, and to which He also promised to send the Holy Spirit, was dependant upon ordaining new Apostles. Knowing this, they apparently forgot to ordain new Apostles, the one thing necessary to keep the Church alive. It is beyond belief.
Actually they are “Joseph Smith-onlyists”. When all else fails this is their fall back.