Must I personally copy or transcribe the Sutra or are there other ways? In particular, if I sincerely have faith and recite the Mantra, will I be able to change my destiny this lifetime? For example, if I am in a relationship with one person but love another, will reciting and printing the Mantra help me marry the one I love? Please kindly instruct me.
I do not recall instructions to obtain those kinds of responses from the Sutras regarding the practice of The Great Compassion Mantra.
I think you are probably referring to the Guan Yin White Robe Dharani in which the Guan Yin Speaks of According to your Wishes Dharani Sutra has instructions such as those to get results.
If one carefully reads the specific instructions, you are supposed to recite the mantra 12,000 times (the more the better) and you will obtain limitless Dharma benefits.
Furthermore, you can magnify the benefits by printing the mantra 1,200 times and widely distributing it. The principle behind it is not so much that you must invest resources to print but rather that you encourage others to recite the mantra which then indirectly generates more benefits for yourself.
I am not sure that the mantra will enable you to marry the one you love. I doubt that the Bodhisattva would get involved in such endeavors because when love becomes hate (which in the United States seems to happen often: we have a 50% divorce rate right now) the Bodhisattva might be blamed for it!
By the way, if one sincerely recites mantras without expectations, one will receive a better response. The only desire that I encourage in my students is that they work diligently toward enlightenment in this lifetime or toward rebirth to the Pure Land. I feel that encouraging any other kind of desire, especially for obtaining spiritual penetrations or responses, tend to nurture greed and will result in less benefit.