Dental cavity crown-re;ated?

Indirectly, maybe. Question is too vague, but i'll address possibilities. If a crown is poorly designed with a gap in the fit on the tooth, a cavity could develop in gap. If cavity remains after tooth reduction for crown, it may continue to progress under crown. If a crown doesn't contact adjacent tooth well, food trap forms which creates a condition for a cavity to occur on adjacent tooth or at margin of crown.
This is unlikely. Crowns (which usually cover all the visible tooth) will give you better protection from decay on that tooth. If your oral hygiene is inadequate (improper flossing and brushing) decay can occur below the crown margin below the gum line. It is not uncommon to find decay on teeth adjacent to the crown again if oral hygiene is not adequate.
Possibly. Large cavities can lead to excessive loss of tooth structure requiring crowns. Even good crowns fail after many years, there is wear and tear in the mouth. Poorly fitted crowns can attract plaque and bacteria leading to decay.
Possible. It is very possible for a tooth which has been crowned to decay on the tooth structure below the crown.
A cavity begins it. All cavities start small... 1 surface of decay. The cavity spreads which results in 2 surfaces of decay. If left untreated the decay continues to spread & becomes a 3 surface cavity. Then it moves on to a 4 surface cavity. It becomes too large to fill the decayed area & a crown is needed. Deep cavities also can lead to root canals. Best to treat the 1 surface cavity & avoid crowns & root canals.