Do untreated baby teeth cavities affect the new teeth coming in?

Yes. Baby teeth 'hold space' for the adult teeth. If a cavity is untreated in a baby tooth for an extended period of time, the space for the adult tooth may be lost. Thereby crowding the adult teeth.
Absolutely. A cavity is a localized hard tissue infection that requires immediate treatment. Cavity may intensify, infecting nerve of tooth resulting in painful abscess. Infection can damage underlying forming permanent tooth. Infection can spread to bone, gums, lymphatic ; lymphatic tissues with the risk of debilitating results.
Not usually. However, I would be concerned that there is a lifestyle issue coming up. The bigger danger is getting infections in the body, particularly heart, from teeth.