Yes, your article can still be published elsewhere, unless you actually do sell it as a sole rights article through FaithWriters. If you sell it to the publisher so that it basically becomes their article to use as they wish, then you can't use that article anywhere else.
For now, though, you can try to sell something through FaithWriters, and be seeking other publishing opportunities as well. However, if you do have it published elsewhere, that should be disclosed to any future publishers.
As for the children's story, I can't help you with that other than to suggest getting a copy of the Sally Stuart's Christian Writers' Market Guide or even the Writers' Market Guide for Children. You should be able to find both those books on Amazon.