If Iceland was uninhabited, and a group of black Africans moved there... how many years for them to evolve to be like white people?

That is a difficult question to answer because skin color is not preserved in fossils. However, there are other indirect ways to figure out. Humans evolved in Africa and not until 60,000 years ago did some Africans migrated out of Africa and populated the rest of the world. Even though Europe was close to Africa, the first migrants did not enter Europe. Most of them in fact followed the coast from Africa all the way to SE Asia and then some even went into Australia. A small group however went into Central Asia (near Kazakhstan and Kyrgyzstan. There they stayed until about 40,000 years ago when a small group migrated into Europe and they were the Cro-Magnon men. Another group of Central Asians migrated east instead and they eventually became the ancestors of the Ainu of Japan, Mongolians, Siberians, and the Native Americans. The Ainu resembles Europeans somewhat with light skin but they are not Europeans or Caucasians. 

Light skin evolved because Europe and north Asia at the time was in the middle of the last ice age and people had to wear clothes to stay warm. In contrast, many people who never left the tropics after migrating out of Africa wore nothing. Wearing clothes protect the skin from skin cancer but it also blocks out too much UV light and prevents the body from making vitamin D. Vitamin D shortage will lead to rickets, which can result in broken or deformed bones or even death. Since light skin allows the body to absorb more sunlight, it prevents rickets. Therefore light skin ostensibly evolved as an adaptation to avoid rickets in a cold environment that requires clothing. For the same reason, the Chinese also evolved light skin. The Chinese evolved from the early migrants who entered China through Burma. We know that the Chinese invented agriculture about 10,000 years ago and then they experienced a population boom. Many of them (mostly men) then migrated to warmer regions, such as southern China and SE Asia. They brought their light skin to these areas and as a result many SE Asians in such countries as the Philippines, Indonesia and Thailand have light skin because of their Chinese ancestry. Therefore light skin evolved no later than about 10,000 years ago at the latest. 

We can narrow the time range a bit further because about 24,000 years ago, the ice age in Europe was at its maximum and most of northern Europe was covered by huge ice sheets and many Europeans had already evolved light skin by then, because they migrated back to the Caucasus region. People from the Caucasus regions have light skin because their descendants are modern Europeans, whose ancestors migrated back to Europe after the ice age ended 13,000 years ago. 

So, the available evidence suggest that light skin probably evolved between 40,000 years ago and 24,000 years ago. Since rickets is such a horrible disease, light skin probably evolved much earlier than 24,000 years ago. Perhaps it evolved a mere few thousand years after the Central Asians entered Europe, as one scientist suggests. May be it was even more quickly than that. Perhaps a few hundred years or even a few generations? We simply do not know for sure.  Other cold adaptations include narrower and taller nose bridges, thin lips, shorter arms and legs, straight hair, more body and facial hair, a rounded torso and more fat under the skin. These adaptations have evolved in the Chinese and in Europeans, so they would presumably evolve also in Africans who migrate to Iceland. Since these adaptations are not as critical as rickets, they probably take a bit longer to evolve than light skin, but no later than 24,000 years ago, because lots of Indians with European ancestors had these same traits. Keep in mind however that people get vitamin D from milk and from the pharmacy, so rickets is no longer a selective force. If Africans migrate to Iceland and they drink milk or take vitamin D pills (or eat vitamin D rich sea food) then they may not evolve light skin at all, even if they have to wear clothes. If they wear hats to keep their head warm, their hair may never evolve to be straight either. 

Reported. Stop asking multiple questions. 

Some researchers suggest that human populations over the past 50,000 years have changed from dark-skinned to light-skinned and vice versa as they migrated to different UV zones, and that such major changes in pigmentation may have happened in as little as 100 generations (≈2,500 years) through selective sweeps.

This is literally what happened. Africans moved into Europe about 40,000BP. They never evolved light skin because of their diets (hunter&gatherers). It wasn't until agriculture and some mass migration from the middle east and North Asia (10-12,000BP) that Europeans became pale.

Infinite

Lamarck was wrong. Mutations happen randomly