To answer some of your questions directly, since you asked a few of them. First off, the mechanics of previewing a scene with the view finder vs. with live view are different. When viewing the scene through the view finder, you are seeing a direct optical projection of the scene as the lens attached to the camera sees it. Light is bent via a mirror from the lens, up through a focusing screen, and projected to your eye via a pentamirror or pentaprism. There are advantages and disadvantages of using the viewfinder, just as there are with using live view. To name two of the most important: focusing can be difficult without a dedicated focusing screen, and you generally can't see depth of field correctly through the view finder. As you mentioned yourself, its also dangerous to look directly at the sun without live view...this is because the intensity of the sun is being directed strait at your eye, and focused more tightly. Such intense light is very likely to blind you if you are not careful.
The reason you don't have phase-shift AF available when using live view is because of where the AF sensor is. Its actually located beneath the mirror that redirects the scene to the viewfinder. The mirror is actually what they call a half-silvered mirror, which only redirects part of the light of the scene to the viewfinder...the rest passes through the mirror, and reflects off of a perpendicular mirror below it. This second mirror redirects the remaining light to the metering and AF sensors, which are in the bottom of the sensor cabin. When you use live view, the mirrors fold up and out of the path of light coming through the sensor. Live view is exactly that...a direct representation of the light focused on the sensor without any obstructions in the way. Without the mirror, the AF sensor can't process the scene, so neither AF nor AF-C focus modes are available in live view.
Live view itself has its benefits. While it limits your auto-focus capabilities, most other functions of the camera are still available. Live view presents a much larger sample of the scene, and also allows the scene to be digitally zoomed in on. This facilitates manual focus or finer focus adjustments after AF. You usually have a composition grid that can facilitate you when you compose a scene. Live view also allows you to see the exact depth of field produced by your aperture setting, assuming you have an aperture preview button. When depth of field is an important compositional factor, live view is the only way to go. Contrast AF is also available in live view, and while it is usually slower than AF, it is still an automatic focus mode that can get you most of the way there. Finally, adjusting exposure with live view tends to be easier. Metering is based off the whole scene being imaged by the sensor, and adjustments to your exposure settings are usually immediately available. Aperture adjustments are usually visible in the view finder, however it is more difficult to see the effect of shutter speed or ISO changes without live view.