why does shutter speed modify picture sharpness/detail? Why do pictures get darker with faster shutter speeds, and brighter with slower shutter speeds?

These things happen because the light sensor in the camera doesn't measure the intensity of light instantaneously, but rather measures all the light received during the entire exposure. You could say that the sensor accumulates or sums the light* for the duration of the exposure. Light is made up of discrete photons, and the longer the sensor is exposed, the more time there is for photons to strike the sensor.

If you want a mental model for how a sensor works, imagine putting a bucket outside when it's raining. If the rain's intensity remains constant, leaving the bucket there twice as long will result in twice as much water ending up in the bucket, right? Or, if the intensity of the rain doubles, you'd expect the bucket to fill up twice as fast. That bucket is like one photosite (i.e. one pixel) on a digital sensor, and the raindrops are like photons. The entire sensor is like an array of several million of those buckets, each measuring raindrops/photons in one particular spot.

So, faster shutter speeds mean shorter exposures, which means less time for movement of either the objects in the frame or the camera itself. Motion blur happens when an object in the frame moves relative to the camera, so that light from a given point on the object is recorded in more than one spot on the sensor. The shorter the exposure, the less movement there is, and the sharper the final image.

Similarly, longer exposures allow more time for light to accumulate on the sensor; each photosite will collect more photons and measure a larger value. Those larger values, taken together, create a brighter image. Just as with the rain, the measurement at each photosite is also influenced by the intensity -- brighter light causes the measured value at each point to increase more rapidly. So, if you want a brighter image, you have two options: increase the light's intensity or use a longer exposure. This is why aperture and shutter speed have an inverse relationship: the aperture controls the intensity of light reaching the sensor. If you want to use a shorter shutter speed without affecting the photo's exposure level, you can increase the aperture to let in more light; if you want to use a longer shutter speed, you can reduce the light with a smaller aperture.

*To be really clear about it, what the sensor really does is to accumulate the effect of the light. When a photon hits a photosite on a digital sensor, it creates a small electrical charge; the more photons, the larger the charge. After the shutter closes, the camera measures the stored charge at each photosite. Film works much the same way, except that the light causes a chemical reaction that increases with more light.