In the United States, "I could nibble on something" is completely natural. It's common, but it's not as common as "I could use a bite to eat."
So is "I beg your pardon." For example, if I accidentally bumped into someone I'd say "Oh, I'm so sorry. I beg your pardon."
"Peckish" is not used in the United States, although most people probably understand it. We would just say "I'm a little hungry," or "I could use a bite to eat" (or "I could nibble on something.")
I have never ever ever ever (in sixty-five years!) heard anyone in real life use the expression "hunky-dory." However, it's the kind of expression that might be regional. To me it sounds like something out of the 1930s. The American Heritage dictionary, however, includes it without any comments. Perhaps it has been revived and I'm too out of touch to know it.