Legend rule: if a player controls two or more legendary permanentswith the same name, that player chooses one to keep and the rest goes to the graveyard.
Planeswalker Uniqueness rule: if a player controls two or more planeswalkerswith the same subtype, that player chooses one to keep and the rest goes to the graveyard.
Black Oath is not a legendary permanent and doesn't have the same exact name as Fallen, and Fallen is not a planeswalker and has no planeswalker subtype, so you can control them both at the same time.
Thirst for Knowledge % to hit artifact
Planeswalker Uniqueness rule: if a player controls two or more planeswalkers with the same subtype, that player chooses one to keep and the rest goes to the graveyard.
Black Oath is not a legendary permanent and doesn't have the same exact name as Fallen, and Fallen is not a planeswalker and has no planeswalker subtype, so you can control them both at the same time.