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If an effect says you can't cast spells, and another effect instructs you to cast a spell, such as that of the ability that triggers when you remove the last time counter from a card with suspend, you won't be able to cast that spell.

If you cast Moderation, you've already cast at least one spell that turn (Moderation itself) so you won't be able to cast any more spells until the next turn. If Moderation comes under your control on a turn you haven't cast any spells, you'll be able to cast one spell that turn.

Moderation's triggered ability works only while it's on the battlefield, so it doesn't let you draw a card when you cast it.