Can large amount space debris be used to block sunlight from falling in a particular land area (about the size of Hawaiian islands)? If so, how much space debris will be required? What will be the environmental effects of this other than just lack of sunlight (i.e will it alter the climatic conditions)?
In short (TLDR): Fourier Optics and Lagragian Point L1
The answers up to now have correctly identified that anything "in orbit" is going to move, and that the earth is rotating as well, thus making a very sticky problem for the evil genius in question, who is trying to block off light only to the island chain of Hawaii (or wherever specific place he has in mind).
However, there is a solution to the movement dilemma: The Lagrangian Points. The Lagrange Point L1, which rests inline between the Sun and the Earth, would be the spot for our evil genius to construct a massive cloud of space debris. The L1 point is formed at the sweet spot between the Earth and the Sun where the orbital period is exactly the same as the Earth, thus allowing the "cloud" to remain inline with the Sun from the Earths perspective. I'll consider this "cloud of debris" to be more of a space engineering mega project, composed of millions of smart satellites, which can make a structure on the same order of size as the diameter of the Earth.
The L1 point is unstable, hence, the satellites must be actively controlled to keep station at their necessary positions, relative to each other and relative to the L1 point. Having now constructed a massive shade, the next issue is forming the eclipse umbra. Light from the Sun will diffract around the edges of the shade(s), and as the Sun is not a perfect point source, the shadow created by a single circular shade is soft at the edges. Hence, Dr. Evil (now our evil genius has a name) can't form a crisp shadow, at least, not likely at 1.5 million kilometers. He could shade the entire planet, provided the shade is large enough, but only shading a specific point is harder.
This problem has a likely solution: Fourier Optics. You've experienced this if you've ever played around with a laser pointer that comes with a set of image masks. Normally, the laser pointer makes a coherent beam that is sharply focused. To create a grid, a smiley face, or some other image, you insert a mask in front of the aperture. This mask uses Fourier optics to construct those cool patterns. The same principles can be used by Dr. Evil's formation of satellites to create a shadow, and having active control over the formation would allow for the shadow to follow Hawaii as the earth rotates.
Yes and no. It depends on what you are looking for. Do you want no light to fall on one specific area ever? Say block all light from Washington D.C.? Not really, you could possibly block light the size of DC but it would move around as the Earth spins.
You have three things you need to deal with when 'blocking the Sun' you have the Earth (with a tilted axis) traveling around the Sun, the earth spinning on it's axis and the 'debris' either orbiting the Earth, or the Sun between the Sun and Earth.
To keep the debris directly over a location it would basically be a geostationary orbit, but it would only block the sun around 'noon' depending on the size of it and the season. In this case it would also act like an extra moon at night as well.
Unless it was very large and blocked a lot of sunlight from a large part of the Earth it would not make a lot of difference. Now if you had something that acted like a permanent lunar eclipse that would start to cause some issues and could start cooling the planet.
There are theorized human projects to do things like this both to increase the energy arriving at Earth and to decrease the affects of global warming, but they would take a concerted effort to perform, not just some Dr. Evil ransoming for money.
The answer to this question, to the chagrin of super villains everywhere I am sure, is no. Specifying an area that targeted on a global scale cant be done in part due to the size of the Sun vs the Earth as well as the atmosphere diffusing light (redirecting it in all directions as it comes through).
I suppose you technically could keep it from getting direct sunlight which could have a very minor effect to climate/temperatures but the temperature impact would be mitigated by diffusion and perhaps more importantly the ocean, since we are talking about Hawaii, now an inland location may be more (minimally) impacted by this scenario.
The cost to create and maintain such a structure would be, dare I say it, astronomical and for the greatest impact you would need it in the lowest orbit possible which...again considering its necessary size would be pretty darn far away, so in the end, totally impractical and as practicality is often moot here, its also not going to be effective in impacting the location in any meaningful way.
I think one answer might be that small unmanned spacecraft are programmed to track down and latch onto space junk, and drag it in between the Earth and the Sun. Once there it could linked to others. Large fields of Space-shade could be moved at once from the ground to make it more or less shady as needed.
It could be the next gold rush, private companies could and would compete for this work. The big question is not if it's possible. ..the question is who will control the shade? "We can't have a "Shade Gap!"