Can I play any kind of card in phase 1?

All cards can be played during Phase 1 and/or Phase 3. However, if a particular card adds to your movement or effects the board in some way you wish to take advantage of during your movement phases (Food and Rune card) then the card would be wasted in Phase 3 since you would have already ended your movement.

There is a card named “Brechhammer” in the German version, “Breaking hammer”, which lets you destroy walls or non-scenario-tokens you pass during your movement. What exactly does pass mean? If I jump over a wall or several walls/non-scenario-tokens (with upgraded base movement for example), do I get to destroy any or all of those I’ve jumped over? Or if I jump on a wall, can I destroy the one I landed on? Or if I’m on a wall and move several spaces on the wall, do I get to destroy each one I passed?

If your character would occupy the same space as the token/wall, while weilding the hammer, you destroy it. If you jump OVER something you are not occupying the space. If you wish to occupy a space with a wall you may smash it before moving onto that space. NOTE you are not required to destroy tokens you step on.