About the noisy neighbour: the others could build a soundproof wall surrounding his property, so that his noise would not reach them. During this building process, he and they would almost certainly reach an agreement.

As for Russia invading the US, if it had no formal government: what would be the purpose for doing so? The US is valuable, to other governments, only for as long as the US itself has a government (with all the power structures that such a government wields over the public). An invading government, in an area without such power structures, would have to take each valuable asset in turn. In order to actually gain anything at all, Russia would have to seize control of every single thing they wanted - an insurmountable task. Especially so, since the people would not surrender without a fight (and, if they were not intensely stupid, they would be well organized - something that can not really be said about the US federal government ).