1. The problem with depending on the government for protection is that you are effectively ensuring its monopoly on defense will continue. This monopoly is bad for a couple of reasons: First off, it is completely antithetical to the idea of supply and demand, as it profits from both customers and non-customers. Second, due to lack of competition, this means you have to hope your government chooses to fund the right things you want, and the aforementioned reason makes this even more challenging. This is why you are starting to see more private security and private police companies recently because of the police failing to properly enforce laws and punish perpetrators.
2. I don't think the situation you are referring to is likely because if this kind of scenario occurred, both groups you are talking about could simply go to arbitration and figure out a solution that will benefit both parties.
3. A government is only as good as the people running it is, and this is why democracy sucks because literally anyone can be a part of it, even the least-qualified people. Even if the government is run by the most-qualified in society, it is still terrible for defending property rights simply because of the loopholes in the law, particularly things like civil asset forfeiture or eminent domain.