Yes! It's an expressive and slightly poetic way of saying this.

yes

Discard does mean the same as throw out, however, the usual English expression would be "rid yourself of doubts". Discarded doubt sounds a bit poetic, like the words of a song.

I have never heard anyone use “discarded” in connection with doubts, but it’s meaning would be perfectly understandable. However, it is common to use “cast aside” or “put aside” or “overcame” as verbs to describe what you are talking about. Example: “She cast aside/put aside/overcame her doubts and proceeded with her bold plan.” As an adjective, we might use “former”: “His former doubts were all gone, and now he had complete confidence in the plan.”