I can't speak all the way through the twelfth century, but I can speak at least for the tenth century (and the ninth if you're interested in that!).

First, I would never consider the paintings during this time primitive, lest we offend art historians. Rather, what we would consider primitive was simply the style of the time. When people look back on modern art, they may find it primitive. Look at cubism.

But on to your actual questions (remember I'm talking about the 900s):

No. They wouldn't have as much political power as kings five hundred years later. This is for a few reasons. At this point, the people were still very fragmented. True loyalties lied to individual kingdoms as opposed kings. So, there were the Mercians, West Saxons, Northumbrians, etc. Even within those kingdoms, common people often were loyal to their local leaders, the ealdorman, as opposed to the king. So while the Anglo-Saxon Kingdoms were first united under Aethelstan and he was the first King of England, he was very much dependent upon the ealdorman to remain loyal to him and to keep the common people loyal as well. That's not to say that the people didn't support Aethelstan and later English kings, but at this point in time, they didn't really feel like an English nation.

The pull of the monarchs in daily depended on how much they wanted to be involved. Again, the common people were more often dealing with local leaders as opposed to the king himself. The king may choose to implement policies that would affect daily lives of the citizens, but it would be up to the local ealdorman to enforce those policies. So in general, no, the king didn't have a large amount of pull. It would have been seen as incredibly rude for him to interfere so closely with what goes on in the land of his ealdorman.

People were definitely nationalistic, but not in the way you're describing. They certainly didn't call themselves British, because they are missing half the island for that. But they didn't really call themselves English either. The kings certainly did, but they would obviously like to accentuate that they were kings over all of the English. Rather these people still would have been thinking of themselves by which of the former kingdoms they came from. They were Mercians, and West Saxons, and East Angles. So it was nationalistic pride, but in a confederate sort of way.

But it's also important to note how kings referred to themselves of this time. There was no King of England. There was a King of the English. There was no King of Wessex, but there was a King of the West Saxons. He wasn't a king of any land, he was a king of a people. And so from this, we can assume that is how the people saw themselves as well. They considered themselves a people who happened to be occupying a certain land.

As we move out of the tenth century (and my knowledge becomes more nebulous), I do at least know that there became more cohesion among the English. They began seeing themselves as a united people as opposed to many separate kingdoms ruled under one king. However, the bit about being more loyal with local leaders as opposed to the king still remains.