If a player cannot fulfill a storm marker requirement - say it calls for a spell and the player doesn't have one - does he have to stop his resolution phase and leave the marker in place, or can he discard the marker without turning in a spell and then attempt the adventure card tasks?

Also, if an adventure card has a penalty of discarding an item - say, an Elder Sign - and the player(s) doesn't have one, can he even attempt the adventure card?

1. If you can't resolve a storm marker effect because you don't have the requirements to discard, then nothing happens, the token has no effect and you keep going with your Resolution phase as normal

2. Same as above, if you don't have the item to discard, then nothing happens

Hope this helps!