Yes take it to a vet to make sure
I wouldn't worry about a little black discoloration -- the body often deposits pigment in tissue that is frequently irritated or rubbed, such as nipples on a nursing mum. As long as there's no pain or redness, or loss of milk, I would not worry!
I'd go for an exam to be sure, it may just be coloration but particularly in unspayed females mammary cancer is very common and a concern.
No, take dog to vets.
I'm not sure if it was always black or not? If it has turned black you may want to go to the vet and make sure it is not infected or dying tissue (necrosis). Is there any smell or other indicators it isn't supposed to be that way? Is it wet or sticky? Has she recently given birth? Does everything else look normal. No fever, lethargy, eating drinking, and acting normal? If it's always been black it is probably just her skin pigment.