The singular regard is correct in phrases like with regard to and in regard to, meaning with reference to, while the plural regards expresses respect, affection, or condolences. So yes, it’s grammatically correct.
Yes, in between Dylan and a, and between York and is
"And looky here—you drop that school, you hear? I'll learn people to bring up a boy to put on airs over his own father and let on to be better'n what HE is."
