Oxalate and CO3 2- as a polydentate

[JinwooLee_1F]

As I was solving 9C.5, I did not get b) and d). For b, can someone explain how one molecule can either be a mono- or bidentate ligand? For d), since there are four Oxygen molecules with lone pairs, shouldn't it be a tetradentate ligand? Thank you for your help!

[Tiffany_Chen 2K]

For d), oxalate is bidentate as there will be two double bonds (these won't bind to the metal as the pi bonds restrict rotation, thus only 2 of the single bonded oxygens can bind at once).

[Maya Beal Dis 1D]

Would it always be the two single bonded oxygens that bond to the central atom? Could it be one of the double bonded oxygens and one of the single bonded ones?

[605208780]

I think it would always be the single bonded ones due to the absense of the pi bond but I am not too sure