Fear and Trembling is subtitled "Dialectical Lyric." What is the significance of this subtitle?

The answer to this question could be treated with great complexity. The work is lyrical throughout, but particularly in the Exordium and Eulogy on Abraham, where Johannes puts his full literary powers to work. The problemata take on a dialectical form, as they address their given questions through a series of alternatives: either Abraham is the father of faith or he is lost, etc. Johannes proceeds through the problemata like a good Hegelian, setting up opposing pairs and mediating between them.

Interestingly, though, Johannes claims at different points in the text that he is neither a poet nor a philosopher. If he is not a poet, what right does he have to claim to write a lyric, and if he is not a philosopher, what right does he have to claim to write a dialectic? It seems he ironically undercuts the very methods he uses to make his points.

What is the significance of the name "Johannes de Silentio"?

Literally, the name means "John of Silence" and it alludes to a character in a Grimm fairy tale who is turned to stone for attempting to warn his master. He is eventually returned to life when the master sacrifices his own children, and then resurrects the sacrificed children. This character thus experiences the repetition discussed in the book of regaining everything he lost. This John, like Johannes, is not a man of silence, but is rather distinguished for speaking up. Perhaps Kierkegaard feared that his warnings against complacent bourgeois life and Hegelianism would be met with a stone-like silence.

Who wants to "go further" than faith? Why is Johannes opposed to this position?

Hegelians want to "go further" than faith, seeing faith as a lower expression of the Absolute Mind than philosophy. Johannes feels that these Hegelians treat faith as something that can be understood by reflecting upon it. He suggests instead that faith requires passion, that one must work toward it. One cannot understand faith by having it explained.