In the Badges page, you can see all the Badges, with a check next to the ones you have. You can also select how to sort the Badges, which ones to filter out.
Now, can I somehow sort the list by times awarded, or for example show only bronze unawares badges?
No, and given that the list of badges is very small, this feature is a lot of effort for very little gain. If you really want to sort/filter the badge data I suggest you copy it into a spreadsheet, or use the data api.