Yes! However avoid using που if the meaning is unclear. Ο οποίος, η οποία, το οποίο, because they give information on gender and number, can easily clarify things.

From the school grammar book: "[...] Χάθηκε το κουτί με τις φωτογραφίες, τις οποίες μου έδωσες χθες (είναι σαφές ότι έδωσε τις φωτογραφίες), αντί Χάθηκε το κουτί με τις φωτογραφίες που μου έδωσες χθες (είναι ασαφές αν έδωσε το κουτί μόνο ή το κουτί με τις φωτογραφίες ή τις φωτογραφίες)."

Because the Greek used the aorist tense, not the present perfect.

Greek's present perfect tense is fairly similar to English's present perfect tense, so you can usually translate Greek έχω αγοράσει to English "have bought" -- and conversely, when Greek does not use present perfect, English present perfect is usually not a good choice, either.

Greek aorist is generally most like the simple past in English.

Why not "This is the watch which I bought."

That is one of the accepted translations.

the app marks it as wrong.

That would surprise me.

Did you take a screenshot of the result screen with the error message? If so, could you please upload it somewhere and copy the URL/link to the image here?