Good topic. Those pointy glass ornaments with an indentation are a stylised star, IMO. They're a kind of glass finial, the sharp bit found on the top of house gables, sign posts and so on whose job was to stop rain water getting in and ruining the wood and became more decorative over time.

When glass ornaments were all the rage for Christmas tree decoration it would have been difficult to create a pointed star and a spike with a fluted bowl was the next best thing.
The fairy must be a derivation of an angel, surely? Maybe from a time when overtly religious icons were deemed improper. We have a large, gold papier mache star my wife made almost twenty years ago before we had kids and indulged in huge real Christmas trees. It looks rather top heavy on the more utilitarian artificial tree we've had lately but she's threatening to go back to a natural tree this year so maybe it'll gain its rightful proportion.

Incidentally, I looked for the kind of traditional glass ornaments my parents had on their tree and they're astonishingly expensive nowadays, presumably because any that have lasted since since the 1930s are intrinsically valuable.