Hello @Sharmochic! Genetics are very fascinating to me, but very confusing too. From what I understand, it's fine to "line breed" quality heritage stock to maintain purity for many generations. Hybrids seem to be stronger and more productive, but offspring will not breed true and further offspring can lose their hybrid vigor but I don't know how that would actually affect hatch rate. Probably with enough separate breeding pens and an organized rotation you could maintain self sufficiency.
This thread may answer some of your questions: https://www.backyardchickens.com/threads/inbreeding-and-line-breeding-poultry.734859/
As far as your neighbor's eggs, their rooster may not have been doing his job. Many roos will only mate their favorites and it's possible the eggs you received were from the "other" hens. Or they didn't have the proper rooster ratio to maintain fertility. Hard to say for sure. Good luck in your ventures!