A TDFC with daybound only transforms if it is on it's front face. If it's on it's back face and still has daybound due to being a copy, it simply remains on it's back face. The game will not become a draw. This scenario is actually quite easy to set up by having Ludevic, Necrogenius  ^Flip exile a daybound card, as Olag, Ludevic's Hubris  ^Flip would be a back face copying a front face.

9/24/2021 It's possible for Olag to become a copy of a card with the daybound keyword ability as it transforms. If this happens, it doesn't transform as it becomes night.

702.145c Any time a player controls a permanent that is front face up with daybound and it' s night, that player transforms that permanent. This happens immediately and isn’t a state-based action.

Animar, Soul of Elements only reduces generic costs. You'd still need to pay .

In addition, abilities apply in dependency order, meaning Mycosynth Lattice will always apply before Titania's Song in Layer 4 so that it can apply to all permanents. Once an effect starts applying within a layer, it will continue to apply in later layers. This means if something explicitly removes Titania's Song's ability, it will do so (most likely) in Layer 6, after the ability already started applying, so it will still remove all abilities and set power and toughness.

Vehicles and Reconfigure Equipment were both in the set, so just saying "Artifact" works to let either be enchanted without worrying about it falling off.

Terror of the Peaks does add an additional cost to opponent's spells, and that cost will be unpayable if there is a Karn's Sylex in play. Note that this only makes the Terror untargetable by spells, abilities will still be able to target it as there is no additional cost for those.

No. Act of Treason creates a control changing effect with a limited duration. It never "gives back" the creature, the effect simply expires. In addition, protection granted by Gods Willing prevents Damage, Equipping/Enchanting, Blocking, and Targeting. It can stop Act of Treason from resolving by making the targeting illegal, but once the spell resolves it no longer targets and the control changing effect can't be interacted with other than creating a new effect that overwrites it (such as by another player casting Ray of Command or activating Homeward Path).