Learn Farsi: من پوشه‌ی بنفش و دفتر خاکستری را خریدم. - I bought the purple folder and the gray notebook.

In Farsi, when you have a list of specific direct objects connected by و (and), the object marker را usually only appears once at the very end of the whole phrase. Putting it after the entire group is much more natural than putting it after each individual item.

Why is there a ی in پوشه‌ی (pooshe-ye) but not after دفتر (daftar-e)?

This is the 'Ezafe' connecting the noun to its color adjective. پوشه (folder) ends in a vowel sound (written with a silent 'heh'), so it needs the consonant ی (-ye) to bridge the gap. دفتر (notebook) ends in a consonant, so it just takes the standard, unwritten ـِ (-e) sound.

Since the lesson is about کدام (which), how would I ask 'Which folder did you buy?' to get this answer?

You would ask: کدام پوشه را خریدی؟ (kodâm pooshe rā kharidi?). Notice that کدام comes right before the singular noun, and because you are asking about a specific folder, you still use the direct object marker را after the noun phrase.

Is the word for gray, خاکستری (khākestari), related to the word for dirt (خاک)?