I don't grow on trees, but I empty your wallet. I happen at the mall or with a click. What am I?

I break the silence with my sound, Most are not glad when my time comes around, I ring to warn or wake you up, Ignoring me can test your luck.

Enquiring minds just have to know, So there's only one way to go, A quiz, a puzzle, interrogation too, What kind of query am I asking you?

Ready to bake But not your food What will you make? Depends on your mood

A cat may wear me for a while, though only out of fright. An empire carved me into stone to honor glorious might.