For Finn's ability to negate losing money/ or discarding items as long as it isn't a cost:

What defines a cost? Is it just the cost of buying things? Does that mean he has endless whiskey, food, tomes, etc? I can understand that you don't lose items/money as a penalty, but it also makes dynamite and holy water fairly strong as well if read that way. What about something like the black cave? encounter where if you discard a whiskey, you get the Tom "The Mountain" something ally?

If he uses dinamyte or holy water as a weapon, then he willingly discards them. If he is instructed to discard dinamyte or holy water as a result of some effect(like uncousciosness), then he may not do so.

If the use or effect of an item requires its discard (like MNT pointed out, or even something like completing a Task or Mission card). Such a requirement will be printed on the card or in the rules for that kind of card.