The correct answers are I am writing to ask if you received my essay., Do you happen to know where my attachment went?, and I would like to know why my grade is a zero.

Indirect questions take their punctuation from the main clause.

• "I am writing to ask..." and "I would like to know..." are statements, so they end with a period.

• "Do you happen to know..." is a question, so it ends with a question mark.

Remember to avoid using do/does/did in the embedded question clause! "Where my attachment went" is correct; "where did my attachment go" is incorrect.