The front element of most lenses is very strong and you can clean it with confidence. Just do not put solution directly on the lens since it is not sealed. I prefer to keep clean the lens and not the filter plus the lens.
Yes and no. Friends personal experience: Lens took an impact to the front, cracked the UV filter, lens good, camera/lens Nikon. It will protect from scratches and impacts as well as protect the filter threads on the lens. If you leave the UV filter on, you do not have to, or rarely have to clean the camera lens behind the filter. With filter or without filter, you clean only one surface. I always put my polarizer(or other filters) on after the UV. The UV filter is rarely removed. This is important if you tend to take your camera to locations that may not be that friendly (hiking, camping, etc). If you are largely doing studio shooting, controlled environments, there is almost no reason to have the UV filter.
NOTE: UV filters do help with better images when photographing outside in bright sunlight. The UV light can trigger some sensors even with the color filter mask that the sensors use. With film, UV tends to ‘grey out’ the sky. With D-SLRs, my recollection is that UV actually deepens the blue on the sky in areas where there are clouds. I would need to double check. It can be subtle and with some of the ‘dynamic range and contrast’ on some cameras.. tricky to detect.
NOTE: With a wide angle, I would recommend a filter with a step ring to prevent vignetting. This does create some problems with some lens hoods.