The math student went into the forest to calculate the height of saplings using this

I am no chum, though I hang beside one. I am not glum, though I wear a somber hue. I ripen while the bees hum, While distant fingers strum, Feasts leave behind a crumb, And many succumb to my sweetness. I am no drum, though hollow at my core. Nor am I scum, though some would stain my name. A stone guards my heart all the same. What am I?

The young Scottish woman loved watching the old US TV show with a furry star

I hold up mountains, yet my top is flat, a table for giants, where clouds come to chat. High above valleys, wide open and grand, a fortress of stone carved out by the hand.

I have no doors, yet I keep you inside. I'm built from the cold, a temporary hide. What am I, where arctic winds cannot chide?