Exposure is measured in stops, with each stop being a doubling of the amount of light.
#2 is the most straight forward application, the length of time the shutter is open directly correlates to the amount of light reaching the sensor/film. So 1/500 * 2 * 2 = 1/125, thus they are 2 stops apart.
#1 is slightly more complicated because aperture is a measurement of diameter. f/8 indicates that the aperture is 1/8 * the focal length of the lens in diameter. The amount of light passing through it is determined by it's area however, the area of a circle, which is pi*r^2. If you solve this formula for r, it's apparent that the area of the circle doubles (one stop), when the diameter (or radius) is multiplied by the square root of 2, not 2 itself. So, f/8 / sqrt(2) / sqrt(2) = f/16, 2 stops.
#3 is both of these principles together. 1/125 to 1/250 sec is half as much light, but f/5.6 to f/4 is twice as much, so these will expose the same.
#4 the time remains constant, so since the aperture f/2.8 is larger than f/16, it will yield more exposure.
#5 24mm is a wide angle, so in order to fill the frame with the subject, you'd have to be extremely close, resulting in perspective distortion. 800mm is a super telephoto, so you'd need to be extremely far away. 110mm is long is enough that you can get a shallow depth of field to blur the background, while also giving a pleasant perspective, since you are a reasonable distance from your subject.
If you do end up needing to put any of this into practice, I strongly suggest picking up the book I linked to. There aren't too many concepts at play on a fundamental level, so if you can get your head around all of them, you'll be prepared for any photographic situation. If you have an electronics background the math should be second nature, that's usually where most people glaze over. (and there are far better explanations of it than the cursory one I've provided)
Good luck!