If you chain “Mystical Space Typhoon” to “Archlord Zerato”’s effect and destroy “The Sanctuary in the Sky”, “Archlord Zerato”’s effect disappears because “Archlord Zerato”’s effect needs “The Sanctuary in the Sky” on the field when the effect resolves, not just when it activates (just like “The Agent of Judgment - Saturn”).
You can activate “Archlord Zerato”’s effect even if “The Sanctuary in the Sky” is not on the field, but the effect will not resolve.
You can activate “Archlord Zerato”’s effect multiple times in the same turn.