A) No you would not have a permanent CEO. No CEO is "permanent," because every CEO's job rests on the future actions of consumers. Insurance companies would have absolutely no incentive to meddle in the affairs of other nations. They are completely defensive. It is just like if I hire private security for my house, would I be afraid that the security company would use its force to rob the 7-11 down the road? Of course not. The private security answers to the consumer, just like every other industry, and I would immediately stop paying for such a security firm if they did such things.
B)Communities would take care of them, just like they did hundreds of years ago, before the government got involved and began the process of destroying communities.
C) Under anarcho-capitalism with every piece of land privately owned there would be no need to regulate the environment. People do not go around destroying what they own, in fact, they would have every incentive to increase their land value. It is just like I do not see people in my neighborhood polluting and destroying the environment, I actually see them planting trees, and plants.
D) Intelligence would be a part of the private defense provided by private insurance companies. They would be charged with the task of knowing all of the potential threats to their customer's private property i.e. if they did not, then they would have to pay huge claims in the event of a terrorist attack. If one firm was not able to gather as much intelligence as another, and disaster for its customer's ensued, then it would go out of business or its profits would go way down.
E) Immigration would be an issue handled by every single land owner. Whether or not you want to hire someone to work for you from another country would be your business. They could go anywhere they wanted on your land. If other people wanted them on their land they could roam around on their land as well.
The mistake you are making is that you want to know every single minute detail of how anarcho-capitalism would work before you are willing to give up your belief in the state. Well the problem with this mentality is that you assume that the state is working in the first place. It is not. In fact, the state has failed to accomplish even the most basic tasks it has been charged with, like stopping crime and terrorist attacks. If I were to make a list of the number of things the government has failed at, it would be 50 miles long. The war on drugs, 9/11, public education, the war on poverty etc. etc. etc. Not only has the government failed in all of these areas but it has caused society to regress as well. It has destroyed many of the institutions that were cherished just 100-150 years ago. Take the family unit for example. The family unit is virtually on the brink of destruction. Divorce rates have skyrocketed, crime has been going up for decades and kids today are dumber than their parents. Why is this? The reason why is that the family unit has been attacked by the government from numerous angles. From welfare to the watering down of the currency, to high income taxation and the public "education" racket.
Hence, we must understand that the government has failed from the outset, not that it "works." Once we realize that it has failed, we must think of why it has failed and if it is to be abolished what can we replace it with. Well, we should most certainly not replace it with another government, this would just eventually bring us right back to where we are today. No, it should be completely abolished and society should become one that is based on pure private property contractualism. If you are still skeptical of whether or not the government has failed, I have a book I reccomend you read. Democracy: The God That Failed.