1-- Chewing gum is overly casual for service staff. Cracking one's gum is even more rude: it means trying to blow a bubble in non-bubble gum-- and all you get is a little sharp 'crack!' or 'pop!' noise.
2-- Facts first, theories second. Honestly, I have never heard it, but just as honestly, it sounds like a saying many might say. Ms Google only gives me a couple of hits on the phrase.
3-- Be bound to win = be sure/confident of winning.
- For Teachers