The literature about K3 surfaces is extensive. Let us consider the fact that the zero locus of any smooth homogeneous degree 4 equation is a K3 surface.

Let $R$ the quotient ring of a homogeneous polynomial in $4$ variables and degree $4$.

I am not being succesfull to find anything related to the study of derivations and locally nilpotent derivations on these sort of ring. What could be a reference for

1. a description of the derivations on $R$?
2. a description of the locally nilpotent derivations on $R$?
3. a description of the automorphism groups of $R$?
4. any condition for the group of automorphisms of $R$ to be finite/finitely generated?