In some comic storylines, Penguin's sexuality might be depicted as such, but it depends on the specific comic and the creative choices of the writers and artists.
The status of Penguin's sexual orientation in DC Comics is rather ambiguous. Different story arcs might hint at various possibilities, but there's no definitive statement of him being gay.
Penguin and Riddler are typically not friends. They often operate independently and may even compete or have conflicts with each other in the comic universe.