Regarding your title,
"About the products doesn't need to be inspected!"
you need a subject for the relative clause. You can't drop the 'that/which'. Also products needs <don't>, not <doesn't>.
About the products. They don't need to be inspected!
About the products that don't need to be inspected!
I think all manufactured products have to go thru some type of inspection or certification. I'm not sure whether, after the standards are set, for some "benign" products, the testing might then rely on a self compliance standard by the manufacturer.
- For Teachers