Is it possible to end the sentence with "det" here, when kroppen has already been identified as common?
No, den/det has to agree with what was found in this sentence. Thus it has to be den above.
Saying "de hittade den" sounds like the opening to the theme of Superman.
What is the diffetence between hittade and hittat?
hittade is like the past simple and hittat is the supine to form the perfect tense