Learn Spanish (Spain): ¿Has perdido la mochila? No, no la he perdido. - Have you lost the backpack? No, I have not lost it.

No, you cannot attach it to the end here. In the pretérito perfecto (present perfect), object pronouns like la must always go right before the conjugated helping verb haber (in this case, he). You can never split the two parts of the verb (he and perdido), and you cannot attach pronouns to a past participle like you would with an infinitive.

Since la refers to the feminine word la mochila, shouldn't it be la he perdida?

Good guess, but no! When used to form the pretérito perfecto tense, the past participle (perdido) never changes to match gender or number. It always ends in -o, even if the direct object pronoun (la) refers to a feminine object.

Why are there two nos in the phrase No, no la he perdido?

The first No simply answers the question, just like in English: "No, ..." The second no makes the actual sentence negative: "... I have not lost it." Notice that this second no must be placed directly before the object pronoun (la) and the verb.

How do we get has perdido and he perdido?