These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
Amazoness Archers: If you activate "Amazoness Archers" and chain "Magic Cylinder", "Magic Cylinder" does the full damage before the -500 ATK is applied; your opponent's other monsters must attack normally. If you chain "Amazoness Archers" to "Magic Cylinder", the ATK is reduced first and then "Magic Cylinder" does damage.
Book of Moon: If you chain "Book of Moon" to "Magic Cylinder" […] to flip the target of any of those cards face-down, the card’s effect disappears. (See "Activation & Targeting Eligibility" in the Advanced FAQ.)
Ordeal of a Traveler: When you activate "Ordeal of a Traveler"’s effect as a chain to "Magic Cylinder", since "Ordeal of a Traveler" resolves first, if your opponent guesses incorrectly then the attack does not resolve and the effect of "Magic Cylinder" disappears. If multiple copies of "Ordeal of a Traveler" are active, their effects are cumulative.
Spirit Reaper: When "Spirit Reaper" is targeted by an effect, "Spirit Reaper" is destroyed by its own effect AFTER resolving the effect that targeted it. For example, if "Spirit Reaper" attacks and "Magic Cylinder" is activated, designating "Spirit Reaper", first "Magic Cylinder" will resolve, negate the attack, and inflict 300 damage to the controller of "Spirit Reaper". Then, after that, "Spirit Reaper" is destroyed by its effect.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.