The only sentence in this chapter that gives me some confusion is this:
Iam inde ab initio Faustulo spes fuerat regiam stirpem apud se educari…
My direct translation: Now from the beginning there had been a suspicion to Faustulus that he brought up royal stock.
I see the educari is infinitive passive with se, but it then takes the object accusative with regia and stirps. I either translated this wrong or there is a rule I’m forgetting with the infinitive passive.
I think what you are missing is that in indirect statement the accusative may be the subject of the infinitive, and that you need to translate the infinitive as a passive, and that apud + pronoun is a kind of stock phrase meaning “with + pronoun” or “at the house of + pronoun.”
Now from the beginning it had been Faustulus’ hope that the royal offspring be brought up at his house.
Ahh. I knew that, but obviously I needed the reinforcement (smacks forehead so hard). Thank YOU 
Yes, most Latin students have a slight dent in their forehead for just such reasons. Nullo negotio…
Yeah, ever since I started learning Latin it has been a whirlwind of exhilaration, confusion, triumph at every step. It helps an autodidact to have reassuring vets like yourself for reference and support. Tibi gratias ago. Progredior!