Do medical devices need to be approved by the fda? who regulates these devices such as an inversion table for example? how can i be sure they're safe?

Yes; see chart: Many organizations, including the fda, inspect & approve various types of medical equipment for safety. Look for a seal of approval on the item or in the literature accompanying the product. Buy from reliable vendors.

Not a Medical device: Yes, actual medical devices are regulated by the fda, but i doubt an inversion table is marketed to treat anything. Most manufacturers go out of their way to be sure to state the it is not intended to treat a medical condition. So you are left with reviews and comments by other users. If the device is truly unsafe and it injures someone, they will be sued for it.