Ok, so I have been living with former hunter-gatherer indigenous groups, first of all.
1. From what I have seen polygamy is more common with sisters (I suspect this is where the idea of “sister wives” comes from). Usually, the man marries two or more sisters, or women who are “classificatory sisters” ie they have been raised as sisters (a bit more complex than that, but that’s basically it). This serves to keep the family together, especially if the parents are dead. Also, because many groups practise patrilocality (so the couple move to the husband’s location after marriage) then new wives can be isolated and upset. The rate of divorce increases as the new bride is taken further from home, but decreases if she can take a sister wife, in the form of an ally from her childhood, with her.
The other time I have seen it is if a close female relative is widowed or orphaned, and she is taken in by a close female family member as a “sister wife”.
The key thing to bear in mind is that these communities often take a shared interest in childcare, which is largely communal. They also swap children for several social purposes, so the child a woman calls her “son” or “daughter” may not be biologically hers. Tracing descent is therefore less important, especially for former HGs, who have very few possessions to pass down to the next generation etc.
Jealousy is not as important as social cohesion here… you practise polygamy to maintain social peace.
You can also see this in Judaism, where a man was expected to marry his dead brother’s wife in order to keep the family together, and in Islam, where temporary marriage is designed to protect a widow or orphan by marrying them to a family member until they can receive their inheritance.
2. HG groups are very, very democratic in general. Everyone must agree to a decision. If they reach an impasse, the group would traditionally separate along factional lines. If not, they keep negotiating. This is more of an issue now that most HGs are settled in permanent villages and cannot escape from each other physically. Divorce is generally permitted in HG groups, but not encouraged.
3. HG groups are usually very small, and polygamy and polyandry are specifically designed to keep families together. A good relationship between the whole band is a prerequisite, and everyone has to get along for it to work. Fun fact: amongst the group I worked with recently, only leaders were allowed to have more than one partner, because it was thought that only group leaders had the interpersonal skills to maintain a harmonious household with more than one spouse. This involved managing ALL of the relationships involved, inclusing those between spouses.