You select the Spell / Trap Cards when you activate the effect of “Mobius the Frost Monarch”.
This effect targets.
If “Level Limit - Area B” is active and “Mobius the Frost Monarch” is successfully Tribute Summoned, “Level Limit - Area B” is a Continuous Spell Card so its effect is applied and the battle position of “Mobius the Frost Monarch” is changed to Defense Position. Then you can activate the effect of “Mobius the Frost Monarch”.
If “Mobius the Frost Monarch” is Tribute Summoned by the effect of “Ultimate Offering” in the middle of a chain (and is not the last step of the chain to resolve), then you have missed the timing on his effect and you cannot activate his effect to destroy 2 Spell or Trap Cards.
If 1 of the 2 Spell or Trap Cards targeted by the effect of “Mobius the Frost Monarch” is destroyed by some card effect before his effect resolves, the remaining 1 card is still destroyed by his effect.