What substantiation should the advertiser have to support these claims?

The advertiser should have to show that the product worked in a clinical trial over a long-term period, and individuals with the same diet and exercise habits and similar body composition who used the belt while exercising lost more weight over the long-term than those who did not wear the belt.

Are any of the representations made in the ad puffery?

Almost all of the language used in the ad constitutes 'puffery' but the most florid claims are these:

"The sauna pro-deluxe advance heat systems sweats away...

No more uncomfortable heated wooden benches. All of the targeted effect of a personal sauna, but better!"
Should the advertiser have included any disclosures? If so, what should they say?

That the product has not been subject to clinical trials and that severe dehydration during exercise can be dangerous.