Can I see shared what a family member is storing on shared iCloud storage?

If you go onto settings, then click on your name, then iCloud, then manage storage your can see what percentage of your family plan is being used up by your family. If you click on Family usage you can see how many Gigabytes each family member is using however I believe you cannot see what each family member is storing on there.

No. See the following from Share an iCloud storage plan with your family - Apple Support

When you share a storage plan, your photos and documents stay private and everyone keeps using their own accounts with iCloud—just like when you have your own storage plan. You simply share the space available in the iCloud storage plan with your family members, so you only have one plan to manage.

However you can still see things that are selected to share, the same as you could if you weren't sharing storage; e.g., shared photos and shared files. See: How to share albums in Photos on your iPhone, iPad, and Mac - Apple Support and Share folders with iCloud Drive - Apple Support