II is definitely false. aabb not generated.
I is true.
$S\rightarrow SS$
$S\rightarrow \epsilon S$
$S\rightarrow \epsilon ba$
$S\rightarrow ba$
--and--
$S\rightarrow SS$
$S\rightarrow S\epsilon$
$S\rightarrow ba\epsilon$
$S\rightarrow ba$
III is correct.
Even though this grammar is ambiguous, we can translate it into an unambiguous version, and DPDA can accept it.
Being ambiguous is the property of a grammar, not a language.
DPDA can't accept inherently ambiguous languages. (ie the Languages for which there's no unambiguous grammar)
This language is fine.
Option B