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If you are not able to delete models you most likely signed up for Analytics (without reading the Terms).
As for the "Approval": models - in general - don't need to be approved, unless they fall into certain categories or you use certain search tags that trigger moderation. But in these cases you are not able to publish them until the approval. So, if on the "My Models" page you see the green caption "Published" on the right side, the asset does not need approval.
If something happens you do not understand, the best practice is to drop an e-mail here : support@cgtrader.com.
If the reason is specific to you, only they can give you an actual answer.
