Sprouts and "better-to-cut-out-parts" in vegetables
Unless you're planning to consume a few kilo of each of them in one sitting, I would say you're being too cautious. Tomato, bell peppers, chilis and potatoes are all part of the nightshades family, and are toxic to some degree. But the poison is in the dose. The amount contained with in the vegetables would mean you'll have to consume an inordinate amount of it for them to take effect.

I cut the sprouts of a potato, I have to peel them anyway. I usually cut away the "crown" of the tomato, mostly because it's tough and I don't want it in the dish. Most of the time, I don't even bother with the white parts of a paprika if I cook them, only in salads for cosmetic purposes I take them out. Onions just get peeled and used. So far, to no ill effect.

[EDIT]

As mentioned by Popup, be wary of green potatoes: Small sprouts or eyes on a potato aren't a problem; Cut them away as you find them. But do cut away green areas of a potato. As the article in the link tells, it's not that the green parts are solanine (the toxic), but rather an indication of areas where solanine build up takes place:


  "What is the green? Actually it’s chlorophyll. Not bad for you at all.
  But the chlorophyll indicates that the potato has been exposed to
  sunlight. And where the potato has been exposed to light is where a
  natural toxin in the potato (solanine) becomes concentrated at harmful
  levels"


No need to discard the entire potato, just get rid of the offensive parts, and when it makes sesnse, i.e.: If you need a microscope to spot it, or if it's the size a pins' head, so to speak, don't worry about it.