Wording of the individual cards in question is the key.
Blessings can be used in any combat check because it is worded as "Discard to add 1 die to a check."
Weapons usually can only be used in your combat check because it is worded as "For your combat check,..." There are weapons with extra options, such as the second ability of a Longbow.
As for which skill is used in combat...
Pathfinder ACG: Rise of the Runelords Revised Rulebook, page 11 wrote:
Most monsters and some barriers call for a combat check. Weapons and many other cards that can be used during combat generally tell you what skill to use when you attempt a combat check; if you don’t play such a card, use your Strength or Melee skill. (A few items that can be used in combat don’t use any of your skills; they instead specify the exact dice you need to roll or the result of your die roll.)