I'm currently taking a course on Europe in the High Middle Ages, and we briefly did an overview of the feudal ystem from the early Middle Ages. My professor emphasized how unpopulated the land was, and how small the villages were, along with how the peasants were very tied to the land. In that case, how did they find someone suitable to marry who was not closely related to them? I apologize if I'm making any incorrect assumptions about how sparsely populated the land was, or the size of the villages.
When the Church finally got to issuing particular injunctions about marriage, the prohibited it if the parties were within seven degrees of consanguinity. Even in the highly populated thirteenth century, this was probably not possible to avoid in most villages; the nobility certainly couldn't manage it. So, the answer to one of your questions is that the rules weren't yet actually rules, and were in any case more like guidelines.
A more important point is that just because there was relatively few people per square mile, it didn't mean that the people were evenly distributed. Villages were near each other, and near the surviving Roman roads. Also, a lot of the original assumptions we've made about the "horizons" of travel have come under attack. Long distance travel did drop off, but short and medium distance travel continued. Finally, although there were major population collapses, we see signs of recovery shortly thereafter. By 700, population was growing once again.
In short, it wasn't as bad as all that.