三人行，必有我师(焉)

Jumping in since I'm here (and I like grammar! :)

I think "[X]是[Y]的" is a fairly common structure in general -- basically, the 的 at the end is turning the whole final part of the sentence [一根棒棒糖不能解决的] into one long adjective. So it's the same sort of structure as if you were to say in English "no cats are blue" or "there's no problem [that] is unsolvable."

没有什么紧张是一根棒棒糖不能解决的

Literally I think this would be, like, "There is no nervousness [that] is such-that-a-lollipop-can't-resolve-it." (ETA: Or just "No nervousness is unresolvable-by-a-lollipop.")