How can I show context free grammars are strictly more expressive than regular expressions with an example?
The canonical example is the language $L=\{a^nb^n\mid n\ge 0\}$. It's easy to produce a CFG for this and it's nearly as easy to show that it's not a regular language. For your first question, note that any regular language can be generated by a left-linear grammar and these are CFGs, so any regular language is also context-free.