Both statements are TRUE.
prerequisite : prefix property.
Stmt 1: DPDA with empty stack method, accepts those languages which satisfies prefix property.
Consider a Regular Expression a*, the language corresponds to this regular expression is L={null, a, aa,aaa...},
here, L does not satisfy prefix property and hence cannot be accepte by DPDA with empty stach method.
Stmt 2: Consider the language L in above explanation.