A: "Avoid 1 Attack" can block any action that is targetting the specific Character (or Battlesite) that the avoid works for.  This action could be a numerical attack, or it could be some effect card like "Hero may not attack for remainder of battle" or "Target must discard one placed card". The key for these effect cards is to look for the word "Target", "Hero", or "Character"; if these words are present, then they can be blocked withan "Avoid" Special.  If an effect card only says "Opponent", however, like some AI's that only say "Opponent must discard one placed card", then they cannot be blocked with an "Avoid" because they are not targetting any specific Character, they are instead causing the other player to do something.

Q: If you play Soul Gem against a target, can that character's teammate  negate the card as a defensive action, and can the card be avoided?

A: Oh sure, there's always an opportunity to defend an attack before it hits, even if it wouldn't be defendable that way after it hits.  Here's the metarule that backs me up on this:

(110) A Special that indicates what can and cannot be played once it hits can still be defended by the type of card it restricts, provided no other restrictions are in play.