1) Why isn't China doing anything about N. Korea? Here, the answer seem to arise out of the post World War II division of Korea into northern Russian controlled Korea and southern American controlled Korea. During the Korean War, N. Korea seemed to decide on their own to attack S. Korea, invading while Russia was abstaining from the UN Security Council meeting with the result the US was able to declare N. Korea had taken aggressive action against their neighbor and invade in force. China joined into that battle, forcing American and South Korean forces back to slightly North of the original border between the two. So the reason China often stays mum, seems to be that they don't want to intercede between power plays by either Russia or the United States as represented by their supported side of Korea. Korea had historically split between the Northern part and Southern part for the beginning stages of their country, so merging the two countries doesn't seem to offer any good benefit, both have access to harbors and relationships with the major powers.
2) Why is China a trading partner with N. Korea? N. Korea doesn't have any other trading partner, for one. For another, it minimizes Russian influence over Chinese territory. For another, it minimizes American influence over Chinese territory i.e. the border between China and N. Korea. Also, immigrants from N. Korea tend to head into China and China has their own population problems without additional people.
3) Why is Kim Jong Un so paranoid? Probably because he feels pressure from Japan, China, S. Korea, Russia and the United States. During the Japanese invasion of China, Korea was the entry point, suffering many lives lost and enslaved.
4) Could Kim Jong Un take a friendlier stance? Probably. Without the direct friendship of one of the three big powers, trade is limited. It begs the question, though, why not play the big powers off seeking concessions and partnership from them all? Such a stance would be no riskier than where he is at.
5) Why the big fuss over nuclear power in North Korea?
Would North Korean nukes prevent them from being overrun? No.
Would North Korean nukes aid power supplies within the country? Yes.
Are their American, Russian and Chinese nukes near North Korea? Probably.
Would anyone gain from the use of nukes in this area? Nope. The extensive damage from nuclear radiation would flood the entire region and affect everyone.
I think the real issue is the cooperativeness of North Korea with their neighbors and the United Nations. Perhaps they should seek friends or just shut up.
6) Are North Korea and Japan just pawns in the bigger struggle between Russia, China and North Korea?
Probably. What's there to gain? Oil in the South China Sea, probable oil in the Yellow Sea.
Looking at "China's Struggle to Modernize" gave me a better idea of Chairman Mao and many of the development changes that occurred in the past.