Answer:
In all these phrases, the narrator— maybe Shelley himself, as the speaker could be some sort of a poet or artist — seems to characterize his ideas as outdated or past their best, like the wilted leaves which drop from the branches in the autumn term.
As the western breeze blows the fallen leaves away throughout the spring to make way for new life, the narrator seemed to assume that perhaps the breeze can also vanquish his dead worries and clear the room for new ideas and new thinking.
The speaker may be experiencing some form of inspiring crisis;
He seemed to believe like his old ways were no more, so as to speak, fruitful and longs for the "new birth" of original ideas and new inspiration.
He hopes the west wind will be able to help himself with all of that.