Probably this question has been asked more than once before. But still. The question is meant from both an in-universe and an out-of-universe perspective. 1) (In-universe): Are Tosk and the hunters part of the dominion, and if so, how do they fit in? 2) (Out-of-universe) Was the creation of the Jem'Hadar concept inspired by Tosk? We see several elements in Tosk that we see in the Jem' Hadar later: living for only one purpose without distraction: to die honorably, needing virtually no sleep, needing no food in a conventional way, the capability to make himself invisible, etc...
Yes, I believe the Hunters and Tosk are members of the Dominion. The Tosk have the same shrouding ability as the Jem'Hadar, and even (somewhat) resemble them. IIRC, both are genetically derived from the same 'original' race. And remember the scene in "Broken Link" where a Jem'Hadar takes the helm of the Defiant? That was supposed to be a Hunter. It got changed at the last minute. Earlier, Hunters were also supposed to appear in "The Search" but that got dropped too. The basic thrust of the gist is, the Hunters are the designated navigators/trackers of the Dominion, and the Tosk were engineered for them (by the Founders) as a gift.
In-universe no connection is explicitly defined during the run of the series. Out-of-universe, Mr. Laser Beam summed it up pretty well.
Another Tosk shows up in, I believe it's called "Rising Son", but I'm not sure there've been any other sightings.
The hunt seems like something that the Dominion would be in favor of. Distract people from caring that they live in a totalitarian state by giving them violent entertainment outlets.
I didn’t know about the whole broken link thing. Was that in the companion? I would have loved to see the Tosk and Hunters return.
I always assumed that the hunt was designed as a training program for the Hunters so they can be better trackers. That's their whole role within the Dominion.
Nothing definitive, but the episode was meant to start sketching out what made the Gamma Quadrant different Alpha. The early idea was a greater use of genetic engineering to create various classes to service society. The Jem'hadar and the Vorta ended up being the unwitting accomplices in the oppression of the Founders, but the idea of genetic engineering in service of the state remained.
I don't think the show ever mentions a link, so in-universe, it's up in the air. I like to think they aren't. Always relating every species to x or y faction makes the galaxy smaller. But that's just my preference.
The script for "The Jem'Hadar" actually states this plainly : 23 NEW ANGLE (OPTICAL) the bushes part... As suddenly four JEM'HADAR soldiers shimmer into view. (This is the same kind of invisibility effect used by Tosk in CAPTIVE PURSUIT. The thought behind this is that the same people who breed the Tosks as gifts to the hunters breed the Jem'Hadar as well.) The Jem'Hadar are genetically engineered soldiers. Unlike the Klingons they have no interest in honor or glory. And unlike the Cardassians and Romulans, they have no love of intrigue or politics. The closest twentieth century analogy would be the professional mercenary, but unlike mercenaries, Jem'Hadar don't fight for material gain and can't be bribed or negotiated with. They are the ultimate professionals. And they look scary, too.
I always thought the Jem'Hadar were one of the most interesting races in the franchise. Ketracel White addiction aside, they are THE most perfect soldiers. "TO THE DEATH" and "ROCKS AND SHOALS" are among my favorites of the series because of the focus on the Jem'Hadar.