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I wonder if it is possible an animal can edit its own DNA based on things it observed with its senses in the environment.

Eg Beetle observes kin dying via termite melee, encodes a potential solution in the DNA for the next generation.

Read about epigenetics. It's not quite as magic as what you describe but it's in the ballpark.

This might (eventually, pending MAJOR ethics committee issues) be possible for humans in a lab.

It's not realistic for beetles.