Ok. Date, distance and activity type looks good. The device should be no issue. It is not particulary old. The risk with older devices is that they do not save the files in FIT format which is a requirement. Easiest way to check is to click "Export original" and see which file is exported. If everyting is ok you should get a zip file with a fit file inside.
It should be in the "Current challenges". It stays there 1-2 days after the challenge has ended.
I think it is too late now to do anything yourself. If you see that you don't get a badge you should right away do a couple of edits to the activity. Every time you do an edit to an activity it will be evaluated for the badge. For challenges you got until noon the day after the challenge has ended to do anything.
Now you will most likely need to talk to Garmin Support.
