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You most likely can find a fan online that will fit.
Show us a picture and measurements of the dead fan.
Then again, the dead fan could explain the issue's you are having, from overheating.
I would cut power to the cam at around sunset, then power it back up a 3-4 hours later, and see if the issue's have resolved from letting it cool off.
Have you tried setting the cam back to factory defaults to see if that fixes issues.