What are these?

[Earth]

Carnelian? Delaware beach...first 5 photos dry, last 5 in water

 

[Moesia]

Do not post images of wet rocks, it is important to see their natural luster.

 

[Eu_citzen]

Would need to see a freshly cracked open, the beach hides the luster. Use gloves & eye protection aside from the hammer!
Doesn't look like carnelian, but sure is quartz-related.

 

[Kray Gelder]

Looks like quartzite - metamorphosed sandstone.