A. I defined the density as the number of persons populating the region.
B. I defined the density as the number of persons that populate the region. or
B. I defined the density as the number of persons that populate the region.
C. After I found the lock key, I packed all the furniture in a huge suitcase, belonging to my sister.
- "present participle" is basically an adjective which modifies antecedent(noun) like "a boy studying English" but there is a comma and it stopped a modifying function and formed a participial construction(I packed all the furniture in a huge suitcase and the suitcase belongs to my sister. >, belonging to my sister.)
- "present participle" is used to make "adverbial clause" "adverbial phrase" in order to shorten.
For example, Because I am tired, I went to bed early.
Being tired, I went to bed early. (Be sure to check out if subjects agree with each other in both clauses)
D. After I found the lock key, I packed all the furniture in a huge suitcase, which belongs to my sister.
', which' emphasizes where the intended antecedent(either all the furniture or a huge suitcase) belongs to. Both "all the furniture" and "a huge suitcase" are singular so readers have no certain clue here. You know "furniture" is treated as an uncountable noun.