There's no set "rules" about being polyamorous, it's more of a community, but it's a community that doesn't include fundie Mormons and probably never will. They wouldn't fit in--polyamorous types are usually progressive vaguely-hippie types and the fundie Mormons are very traditional and quite frankly sexist (and don't always respect age of consent, etc., which polyamorous people do).

A lot of people have the idea that any type of polygamy is inherently sexist, and while that's true for traditional polygamy, it's also true for "traditional" monogamy. The historic Mormon polygamy that the fundamentalists get arrested for practicing was indeed sexist, but so were the 19th century monogamous marriages practiced by most other Americans. Contemporary monogamous marriages aren't nearly as sexist, and there's no reason contemporary polygamous arrangements--i.e. polyamory--are necessarily sexist, either.

Polyamory (and the various "open relationship"/non-monogamous lifestyles related to it) are less tied to the ritual of marriage and are often more equitable to women than traditional polygamy. I actually know some polyamorous people who live under the same roof and make babies, for instance. But some people just choose not to mind that much when their partners have sex with someone else, as long as it's safe and consensual. As I said, there's no set rules, other than it has to be safe, sane, and consensual for all parties involved. Which is worlds away from fundamentalist nutjobs in Utah marrying dozens of 13 year old girls.

Not really, since they're totally different communities, and as far as I know, the fundie-Mormons don't actually claim to be polyamorous. At the risk of coining another poor metaphor, it's more like the difference between kosher and halal--sure, in both cases you're not allowed to eat pork, but Muslims wouldn't care to say they keep kosher, Jews don't particularly care if their food is halal, and they're completely separate groups of people. And there's a lot of differences, too.