Can I use sprouting vegetables? Are they poisonous? When cooked, does the sprouting have an effect to foods taste?
Can I use my potatoes or carrots if they already has some roots...? How about when my onion is sprouting?
I'll second NBenatar but with a bit more info:
Carrots, onion, and garlic aren't dangerous when they sprout but they use their sugar reserves to make the sprout. They go downhill very fast and get rubbery and unusable. Whenever garlic or onions sprout I just plant them and use the greens instead.
Potatoes are a little different. Even after sprouting they can still have usable parts for some time. The green portions of a potato are toxic (not enough to be scary but I've heard they will make you sick if you eat enough). It's worth cutting away the green parts if the potato isn't soft yet.
While root vegetables are generally safe, if somewhat past their prime, when sprouting, potatoes are an exception to this. The shoots, and any green parts of the potato are mildly toxic, and should be removed.
On the other hand, with seeds (as opposed to root vegetables) sprouting is actually good for you. For example, if you have beans or chickpeas, or even wheat, that has sprouted, they are edible and quite tasty. In fact, people often sprout them on purpose to eat, as the sprouting makes some changes to the seed's proteins which makes it more beneficial to the human body.
Beansprouts and wheatgerm are more common examples of this, but it holds equally for any bean or lentil.