I have two questions concerning the existence and uniqueness of enhancements in the following cases: i.) Let $A$ be a finite dimensional $k$ algebra of finite global dimension. Does the triangulated category $D^b(\mathrm{mod}A)$ of finitely generated $A$ modules admit (unique) enhancement?
ii.) let $X$ be a smooth projective scheme over $k$. Then $D^b(X)$ has a unique enhancement. What is about admissible subcategories $R\subset D^b(X)$...Do they have (unique) enhancements?