Literally, a one-trick pony is a small horse that has just one trick, or skill.
Fall on the face is a metaphor for making mistakes, often in a dramatic, even embarrassing fashion.
Soul-searching means a close examination of one's heart before making a decision.
The full expression is the proof of the pudding is in its eating, an American expression, to be sure, judging from its simplicity.
First of all, true to form simply means as expected. In other words, there’s nothing unusual.