I'm so new to the concept of square foot gardening that I think I just made a pretty silly rookie mistake.

I had just finished treating my entire yard with Scott's Turf Builder "Weed & Feed" before it occurred to me that was probably a terrible/dumb (terribly dumb?) idea -- considering included was the sunny spot I was planning to build a raised garden bed. I assume there would be health concerns with the Weed & Feed chemicals getting into a vegetable garden. What should I do to address these concerns?

My specific questions:

1. Is it a bad idea to put my raised bed in a spot on my recently treated lawn – even if I put lay down cardboard underneath?
2. I've read that laying down cardboard will kill the grass and weeds, but should I now consider digging up the turf and/or doing something else to the area to mitigate the concerns mentioned above?
3. Am I being overly paranoid?

Thanks!