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a) The Profoto dishes are excellent and I wouldn't hesitate to recommend them. (Well, I'd hesitate to recommend the silver one unless you know it's exactly what you want.) Other options include the excellent Mola dishes, or if you need something more portable, Chimera's new Octa Plus 2 collapsible beauty dish works rather amazingly well. Any modifier with a Profoto mount will fit any Profoto head, though you'd want the optional domes if you were using a D1.
b) More or less. As with any light, you don't have to point it dead at the model. You can feather it, you can bounce it off the wall, etc. The Profoto dishes only go on one way and don't zoom; third-party dishes don't have a stop and you'll have to experiment to find their sweet spot.
c) Yes. You can use it alone, you can use it with fill, you can use it as part of a ridiculously complex multi-light setup. All of those options are common, it just depends what your vision and preference is. Personally, I love a dish as key with no fill.
d) In my opinion? You bet your sweet bippy. If I could only shoot with one modifier for the rest of my life, it'd be a beauty dish. Especially if a grid doesn't count against my single modifier limit.