Can I see a list of donations per donor?

Yes, there are two ways to do this:

Option 1

Visit the Donation reports screen, select Donations (by Donor).

Choose the donor of your choosing and a date range to display that donor's giving within the specified time period.

Option 2

Alternatively, you can visit 'Manage Donors' from the sidebar menu, click on the donor and then click on 'Recent donations by...'

To better understand the Manage Donors module, please view the module overview here.