No. There is no association between gynecomastia and offspring with larger breasts. Although there may be many “causes”, most cases are idiopathic (no specific cause). The use of certain medications, drugs, organ dysfunction (kidney or liver), hormonal imbalances etc. May also be causative.
Gynecomastia. There is no known correlation with gynecomastia and daughters with larger breasts unless you are considering the larger breast size seen in both men and women who are overweight. That excess fat will give a male, even with a small gland component breasts. The fat will make a female breast bigger. Pseudogynecomastia is a poor term as there is a gland component in every breast.
No. Absolutely not. I don't know where you could have heard that.
Fat in Families. There can be genetic traits that tend to obesity. However, they can be sometimes hard to separate from social behavior that can also be trend setting in family groups. When such issues are present, father, mother and children can all have larger breasts.