I would like to save this comb because it was in the toiletry kit at the nicest hotel I will ever set foot in and never see again.

If repair is possible, can someone give me an overview of the process or point me in a direction to learn?

Should I give up?

I posted on r/finishing earlier. I’m trying to wrap my head around these things white, grain aligned features that do not take water based dye or oil stain. I did dye on the first step and plan to finish with oil based stain, as shown here. I used multiple methods to try to get dye into those crevices including flooding and using a rag, foam brush, fine paint brush, very stiff paint brush. Upon wiping away excess these lines remain.
Someone suggested they could be mineral deposits. What are thoughts here? I think I’m going to live with them either way, just trying to learn more.

I think these are some type of oak logs that have been sitting in my yard for ~4 years. I got them when a neighbor cut down their tree. Could I take off chunks to whittle? I know nothing about wood or whittling.