Mark'd out by dangerous parts he meets the shock, And fatal Learning leads him to the block. (171-172)
Even scholars—people who devote their lives to learning and study—face the danger of being killed for their work and their ideas. Hiding in the library isn't going to save us from death, unfortunately.
Around his tomb let Art and Genius weep, But hear his death, ye blockheads, hear and sleep. (173-174)
In this quotation the speaker suggests that "Art" and "Genius"—personified as weeping people—regret the scholar's death. Everyone else ("blockheads") doesn't realize what a loss the death of the scholar is.
The baffled prince, in honour's flatt'ring bloom, Of hasty greatness finds the fatal doom, His foes' derision, and his subjects' blame, And steals to death from anguish and from shame. (251-254)
The Bavarian prince (Charles VII) has a really bad death. He's insulted, he's blamed, and he dies from all of his pain. Johnson's speaker suggests that fame and greatness often lead to a terrible end.
For faith, that, panting for a happier seat, Counts death kind Nature's signal of retreat (363-364)
This is the first time in the poem in which death is spoken about in a positive way. Johnson's speaker suggests that when we have faith in God, we can look on death as a good thing—it saves us from all the unhappiness of earthly life.