Yes

Yes, you always have to do as much as you can. For instance, if you have to lower your Weapon level by 3, and you only have Weapon level 2, just lower it by 2. You may then take a Wound as the result of the rule of unfulfilled demand, unless the card specifies otherwise. The exception is if there are othe consequences specified: for instance, if a card tells you to "discard 2 wood or take 1 Wound if you can't", and you only have 1 wood, keep the wood and take the Wound.