Is this formal grammar context-free (CFG) but not context-sensitive (CSG)?
Context-free languages are context-sensitive languages; therefore, if there's a valid CFG for a language, then there is a valid CSG for the same language. Depending on how you define CFGs and CSGs, it's possible that a CFG may not count as a CSG. It's quite often the case that CSGs aren't CFGs, even if the CSG generates a context-free language. Basically, even if CFG does not imply CSG, it is still true that CFL implies CSL. That's the confusion: the Chomsky hierarchy implies things about languages.

If your definition of a CSG says "No ϵ  transitions", you're right. If it says "The only ϵ  transition can be S→ϵ , then you are right. If it doesn't say something specifically excluding α→ϵ , then you're wrong. It's a matter of how you define what consistutes a valid CSG, which sounds obvious, and in fact is.