When the dremmel is used on the beak, light and quick placement of the dremmel on the areas of the beak to be trimmed should be performed, because IF the dremmel is allowed to stay in one place for too long, it creates a 'hot spot' which the bird will feel on the beak. It's kind of like putting a dremmel on your nail bed (for those that have acrylic nails).
If the bird is given a lot of chew toys, especially, safe wood for them to chew on, the beak will stay in good condition.
I think the noise of the dremmel scares the bird, more than the procedure, but again, it is important that the person doing the trimming does not hold the dremmel in one place for too long. Short and light strokes will not cause the bird to feel a 'burn'.
If the nails are trimmed too short, yes, it will cause the bird discomfort and pain, so taking a little off the nail is best. I like to use a dremmel for the nails too. Just touch the pointed end of the nail with the dremmel, not taking off too much because the nails are what the bird uses to hold on to things too.