As a young woman living in the west, what's my main responsibility and role in time of Ghaybah?
I guess among the first steps is to know more about the Imam Aj. Any important details that you want to share?

And how can I gain stronger faith and spiritual soul? Or if there's any typical boundary that one's should overcome?

There are many roles and duties for a woman waiting for her Imam ajfs. One of the most important duty is to know your Imam and what he expects from you. This can be attained through Taqwa and Godconsciousness.
Read books on the 12th Imam as and listen to lectures that will inspire you to do more for Allah and His final Hujjat