I think there is no zero percentage house edge gambling sites are there. Because it is not worth for site owners. If they give 0% house edge then why simply they invest a lot of money to create sites, it is no use. Safedice site I don't have any idea about this site. Let me check once and later I will share my experience. But I think there is not

I think that that there may not be a single casino who are not getting any edge, because thay have to run the casino and for that they have to keep some edge, but the edge should not be a big one, so that gambling can easily visit your site and use it for playing gambling.
Casinos may have the only way to make money and that is to get some percent of edge from the gamblers. The only difference is that some gambling sites get a less percentage while the some take a big one, i think depending on the status and ranking of a casino.