Yes, as in
- Tone of voice: He said it in a tone that made her angry. = Er sagte es in einem Ton der sie verärgerte.
- shade of color: I like the tone of blue in this carpet = Mir gefaellt der Blauton in diesem Teppich.
- At the tone of the bell - Beim Klang der Glocke.
No, I think they are unrelated. You can nonetheless associate them if it helps you remember them, though!
"Ton", as in clay, comes from the Early Modern High German "tahen" or "than". [Source]
"Beton" comes from the French "béton" and maintains the meaning (concrete) of the French word. [Source]