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Counters on Crawling Barrens remain on it when it stops being a creature. If it becomes a creature later, they'll apply to it.

If this becomes a creature but you haven't controlled it continuously since your most recent turn began, you won't be able to activate its mana ability or attack with it that turn.

Unless Crawling Barrens is already a creature, its second ability causes the +1/+1 counters to be put onto a noncreature land. Abilities that apply or trigger when counters are put on a creature you control won't do so.

You can activate Crawling Barrens's second ability even if it's already a creature.