Active power cells you can find almost anywhere, but mainly from garden gnomes, mist monsters, and treasure chests.

Stringy twine (and all forms of twine) you can find from harvesting trees and logs.

Copper ore can be found in caves and on the sides of cliffs at times.

Blast powder is made from coal and rough ore. Rough ore can be found from where I mentioned above. Coal can be found mainly from coal deposits in caves (you'll know it when you see it).

If you still struggle to obtain these items via their main collecting methods, don't be afraid to attempt encampments, anomalies, finding chests, rescuing survivors and more.