Welcome!
"dagger" I'd say is a fantasy item, not native; the other is perhaps a camel-whip or prod; I'd be thinking Middle East.
If it is impossible to tell whether it was carved to represent an owl, or a cicada, or a scarab...then maybe it is just imagination that makes it...
I'll offer a skeptical viewpoint: I think it is just a rock. The carved Chinese items linked above look like carvings; this does not, and does not...
I like "onyx." But I could be wrong.
I'd think the larger item would be a decorative tip for a sheath?
I'd think so, yes.
I think the material some posters are referring to can be called fiber optic glass, though it has other names also; it is the same material used...
I agree with Jivvy; and wonder if these might be engraver's tools (burins) rather than awls; if so I think they might have a "diamond-shaped" tip....
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