Line 4: “Keel” has multiple meanings. The first is the part of the ship that goes along the underside that gives the ship stability in the water. This usage really doesn’t make much sense, though, because one can’t see a “steady keel” unless the boat has fallen over. The other use of keel here is as a synecdoche. The keel, a part of a boat, is used to represent the whole boat. More importantly, "the steady keel" lets us know that, despite its rough trip, the ship (like the nation) remains steadfast and true.
https://www.shmoop.com/o-captain-my-captain/ship-symbol.html
Because he fought mythical creatures & the story is far from fiction in multiple ways.
The Tragedy of Julius Caesar deals with the themes of fate, betrayal, and honor, among others. The chief conflict of the play centers on the conspirators' hatred of Julius Caesar's increasing power, which could lead to his becoming king and to the dissolution of the Republic. This tension is about power, one of the play's themes. Also, the men who will assassinate Caesar are his friends, and the play explores the limits of that bond as it is tested by ambition and power.
number 2 in question 1, and number 4 (sorry if it was not useful)