MMmmmh I think that EVERY event is discarded unless it explicitly states that it lasts for X turns. If they wanted the Sliding Walls to be "permanent" they would have designed it as a place... which makes a lot of sense

The same holds for the Horse Thief. If they wanted it to be "permanent" they would have made it a Stranger.

Notice also that in Talisman it is very rare to have an adventure card that can remain face-up to provide only a bad effect . It is against the spirit of the game.

(There are some completely negative cards that can remain face-up, like the Leper, but they provide additional mechanisms that allow for some excitement/fun beyond the simple "avoid this space")

About the Demigod: good question. I never wondered if it remains if you can't take a spell because whoever draw it was always able to take a spell.