the answers to your questions can be found within existing rules.
As the subject line indicates, what exactly is a "creature" by definition? Are all enemies considered "creatures?"
Check base game rulebook, page 10 (red box "Creatures and Enemies"):
Some cards and special abilities refer to creatures and Enemies.
An “Enemy” is any Adventure Card with the word “Enemy” in the card type box.
A “creature” is any encounter (other than a character) that attacks with Strength or Craft. This may include Enemy cards and also Events, Strangers, Places, Spells, and board spaces.
If so, can a creature have its Strength or Craft reduced to zero?
Yes, but this doesn't apply to the +1/-1 given by the Time Card (see next answer)
Would the effects of Day or Night affect the trophy value of a creature?
No, check the Blood Moon rulesheet, page 2:
During the Day, each creature subtracts 1 from its attack score during battle and psychic combat (to a minimum of 1).
During the Night, each creature adds 1 to its attack score during battle and psychic combat.
If a character fights two or more Enemies at the same time, each Enemy subtracts or adds 1 to the attack score depending on whether it is Day or Night.
"Attack Score" is not Strength or Craft, as per base game rulebook, page 10:
The character’s attack score is the attack roll plus the character’s Strength, plus any other modifiers that may apply.
(I really wish FF would update the FAQ and Errata to include all of the latest expansions.)
I wish it too, but the answers to many questions are already given by the existing rules, provided you know them well before playing or check them regularly if you have doubts. Don't underestimate the words, usually they're the key to undestand the effects of a card, especially when keywords referenced in the rulebook are used.
Edited by The_Warlock, 04 July 2014 - 12:21 AM.