The bible verse that Harriet Olson recited to Caroline Ingalls and Charles Ingalls is Proverbs 16:18 which says, "Pride goes before destruction, a haughty spirit before a fall."
Ms. Beadle says that she would buy some paper slate for Laura Ingalls in exchange for when Ms. Beadle needs to buy chalk needs to buy chalk, Laura Ingalls would buy for her.
What happened to Nellie Olson when Nellie Olson called Laura Ingalls' dad, Charles Ingalls, a smelly old horse to Laura Ingalls is that Laura Ingalls punched Nellie Olson in her nose causing Nellie Olson's nose to bleed.