Right word for the sentence-English help "The children had (DRAWN) pictures on the ground"?

Yes. Here's how you find this out. In any good dictionary, when you look up a verb (such as "to draw"), you'll find the verb's three principal parts: the infinitive, the simple past tense, and the past participle. In this case, "had _____," you want the past participle. If you look up "draw" you'll see that the principal parts are "draw, drew, drawn." So you want "drawn" here.

Possible alternatives which avoid possible confusion of medium would be: created, constructed, formed, assembled, etc. I'm sure you could get away with drawn, but if you're looking for an alternative, those should work.