The red one could be Rhode Island Red, the black one looks like a mutt but also looks like a black sex links. Hens eating eggs is difficult to break, try wooden eggs and or ceramic egg where she lays so when she pecks them will be hard. Also collect eggs as soon as possible to to discourage egg eating. On your q about being broody, certain breeds are broody especially the heirloom ones. I got over 40 hens (15 different breeds) and with almost 5 years of chicken keeping only 3 went broody on me (Australorps and Black Copper Marans and a white leghorn that’s not suppose to be broody)