Does the Bad Weather affect other battles?
Yes. Play of a Bad Weather card to negate a Poison Gas! card nullifies all subsequent Poison Gas! cards in any battle for the remainder of this player turn.
Does Bad Weather played to downgrade an offensive nullify Poison Gas for all battles?
No. A Bad Weather card played to downgrade an Offensive card has no effect on Poison Gas! cards. Playing a Bad Weather card can be used to downgrade an Offensive or negate Poison Gas!, not both.