The Home Inspector has no authority to require any of these ?problems? to be corrected. On the other hand, if you are still in the process of negotiating the purchase, you could request the seller to deal with the problems.
To answer your first question, the code was first published in 1897. But that is not what you need to know. Rather, you need to know whether the requirement for a receptacle outlet on an island was, or was not, in the code that was in effect when the house was built. All I can say is that my oldest code version is 1999, that this rule was in effect at that time, and that there is no indication (revision lines in the margin) to show that the requirement had been changed between the 1996 and 1999 editions. I infer that the island was required to have a receptacle outlet, when the house was built.
As to the light above the tub, that area is considered a ?damp location,? or perhaps even a ?wet location.? Light fixtures in such areas are required to be constructed in ways that make them safe in the presence of moisture. In fact, they must be marked by the manufacturer as being ?suitable for wet locations? or ?suitable for damp locations.? That requirement was also in effect at least as far back as 1996. I tend to doubt that a fixture that has a bare bulb exposed would have been so labeled by its manufacturer.
Bottom line: The issues raised by the Home Inspector are valid. The first one is less of a safety concern than the second one, but both have a bearing on safety. I agree with Bryan, that you should arrange for a licensed electrician to look into the situation for you. Whether you can get the seller to pay for the work is another matter, but I think these issues should be resolved before you move in.