QI have this follower on my field, and an opponent plays Craig, Wizard of Mysteria. What happens?

AThis follower's ability would prevent the card draw from happening, so your opponent would simply discard a card.

QIf I have this follower on my field, can an opponent play cards that draw cards, such as Insight?

AYes. However, this follower's ability would prevent the card draw from happening.

QIf I have this follower on my field, can an opponent add cards to their hand from their deck with search effects or effects such as, "Look at the top X cards of your deck. Add 1 from among them to your hand."?

AYes, they can. Adding cards to hand is not considered drawing cards.

QI have this follower on my field, and my opponent has an evolved Ginsetsu, Great Fox and a One-Tailed Fox. Since Ginsetsu, Great Fox's ability increases Yokai followers' damage dealt by 1, how much damage would my leader take if my opponent attacked me with a 1-attack One-Tailed Fox?

AYour leader would take either 0 damage or 1 damage, depending on your decision. When there are multiple abilities modifying damage dealt, the player receiving the damage decides the order the abilities are applied. In this case, depending on the order, the final damage taken can be calculated either of the following 2 ways:

1. Your leader takes 1 damage because you decide to apply Ginsetsu, Great Fox's ability to increase the damage dealt by 1 first, so the One-Tailed Fox will deal 2 damage before this follower's ability reduces the damage dealt by 1.

2. Your leader takes 0 damage because you decide to apply this follower's ability to reduce damage dealt by 1 first, so the One-Tailed Fox will deal 0 damage before Ginsetsu, Great Fox's ability increases the damage dealt by 1. However, Ginsetsu, Great Fox's ability only takes effect when damage is dealt, and 0 damage doesn't count as dealing damage. Thus, the ability doesn't take effect and the damage taken by your leader remains at 0.

QIf I deal 1 damage to my leader with an ability while this follower is on my field, my leader doesn't take any damage, but does Sanguine still become active for me? Does it count toward the number of times my leader has lost defense this turn?

ANo, and no. Both abilities only count if your leader actually loses defense.

QIf I pay the cost of Demonium, Punk Devil's activated ability while this follower is on my field, do I still give my leader -2 defense?

AYes. Giving -2 defense isn't the same as dealing damage.

QIf I play Dance of Death and select an enemy XIV. Luzen, Temperance with 5 or less defense, do I deal 2 damage to its leader?

ANo, you would do 1 damage to its leader. Dance of Death deals 5 damage to XIV. Luzen, Temperance, bringing it to 0 or less defense, but it isn't destroyed until after Dance of Death is fully resolved, so its ability is still valid when you deal damage to its leader.

QIf I play Fiery Embrace with Spellchain (10) and select an enemy XIV. Luzen, Temperance, do I deal 3 damage to its leader?

AYes. By the time you resolve "Deal 3 damage to that follower's leader," XIV. Luzen, Temperance is already destroyed and no longer on the field, so its ability is no longer valid.