Step 1: Examine each statement.
Statement A is correct.
Brown algae reproduce asexually by
\[
\boxed{\text{biflagellate zoospores}.}
\]
Statement B is incorrect.
Sexual reproduction may be
\[
\boxed{\text{isogamous, anisogamous or oogamous}.}
\]
It is not only oogamous.
Statement C is incorrect.
Food is stored as
\[
\boxed{\text{mannitol and laminarin}}
\]
which are reserve food materials and not simple carbohydrates.
Statement D is correct.
Major pigments are
\[
\boxed{\text{chlorophyll }a,\;c,\;\text{xanthophylls and carotenoids}.}
\]
Statement E is correct.
The cell wall consists of cellulose with an outer gelatinous coating of
\[
\boxed{\text{algin}.}
\]
Step 2: Choose the correct statements.
Hence, the correct statements are
\[
\boxed{\text{A, D and E only}.}
\]
Therefore, the correct option is
\[
\boxed{(C).}
\]