The correctly punctuated sentences in the given context are:
B. The friend—whom I met at camp—will be attending my school this year.
C. Gabriel will travel to Peru (where his mother was born) next month.
D. Bears in Space—which is my favorite movie—is on at eight o’clock tonight.
E. Charlie, my oldest cousin, just got a job at the car wash.
A. Apples which come in many varieties are delicious raw or cooked.
This sentence is incorrect because it lacks a comma before "which." The correct punctuation would be: "Apples, which come in many varieties, are delicious raw or cooked." The clause "which come in many varieties" is a non-restrictive clause and needs to be set off by commas.
B. The friend—whom I met at camp—will be attending my school this year.
This sentence is correctly punctuated. The dashes set off the non-essential clause "whom I met at camp" appropriately.
C. Gabriel will travel to Peru (where his mother was born) next month.
This sentence is punctuated correctly. The parentheses correctly indicate that the information "where his mother was born" is supplementary and not necessary for the main sentence to make sense.
D. Bears in Space—which is my favorite movie—is on at eight o’clock tonight.
This sentence is also punctuated correctly. The dashes appropriately set off the non-essential clause "which is my favorite movie."
E. Charlie, my oldest cousin, just got a job at the car wash.
This sentence is punctuated correctly. The comma after "Charlie" and before "my oldest cousin" properly indicates that "my oldest cousin" is a non-restrictive appositive that provides additional information about Charlie without limiting the noun.
In summary, sentences B, C, D, and E are punctuated correctly, while sentence A is not.