What is the connection of the two parts of the verse?
Brachos 60a: Whichever way we expound this verse, it means the same. We can expound it from Reisha to Seifa -- he does not fear bad reports because he trusts firmly in Hashem. 1 We can expound from Seifa to Reisha -- one who trusts firmly in Hashem will not fear bad reports.
Radak: This is the opposite of the Rasha - "Kol Pachadav b'Aznav" (Iyov 15:21). When a Tzadik hears a bad tiding from his children or relative in another country, or if he hears that enemies are coming against him, he does not fear. His heart is proper, and he trusts only in Hashem, and not in his wealth or strength or many lovers and relatives.
Malbim: One would fear if his heart was not proper. He would fear due to his sins, or his evil ways - he harmed people, and they will take vengeance. One whose heart is proper does not fear mishaps that occur, or evil due to the Ma'arachah - he trusts in Hashem to change his Mazal for the good.
A case occurred, Hillel was traveling and heard a scream in the city; he said, 'I am sure that it is not from my house.'
What is "Nachon Libo"?
Rashi: His heart is faithful to his Creator.
Refer to 112:7:1:2-3.