“I think I don’t need anything” / “I don’t think I need anything”
なる means “to become” and is often paired with に when what something is becoming is a noun or な adjective.
That’s the adverbial form. The way you say that something “becomes [い adjective]” is to put it in the adverb form (change い to く) and then follow it up with なる.
あつい - hot
あつくなる - to get hot
Those are fine grammatically, though つもり sounds a bit stiff for daily plans. 予定 probably sounds more natural.