Labor conditions and pay are theoretically covered under fair trade.

> How harmful is the product to the environment (manufacturing through disposal)

This one is more in line with Cradle 2 Cradle: https://www.c2ccertified.org/

> Is the product I'm buying reasonably advertised.

I'm unfamiliar with this organization, but a search popped up the Trustworthy Accountability Group: https://www.tagtoday.net/certified-against-fraud-program/

I didn't find anything on my first page of results for certificates of non-subsidisation.