These question rounds are all lists - for more information on how list rounds are usually adjudicated and scored, please check out the "question formats" page here. Most are from past Varsity quizzes and are thus arranged by the year they were asked.
2. Named trees in Tolkien (note that multiple names for the same tree will not count as multiple answers)
Carnimírië, Celeborn, Galathilion, Hírilorn, Lassemista, Laurelin/Culúrien/Malinalda, Niggle’s Tree (or words to that effect), Nimloth, Old Man Willow, Orofarnë, Telperion/Ninquelótë/Silpion, The White Tree, The Party Tree, The King’s Tree (Smith of Wootton Major)
2015
1. Rivers of Gondor (those named on the main map inserted at the end of LOTR and within Gondor, including rivers acting as borders, at the end of the Third Age)
Anduin/Great River of Wilderland/Langflood, Poros, Harnen, Lefnui, Morthond/Blackroot, Ciril, Ringló, Gilrain, Serni, Celos, Sirith, Erui, The Mering Stream, Entwash/Onodló
2. Kings of the Mark
Eorl (the Young), Brego, Aldor (the Old), Fréa, Fréawine, Goldwine, Déor, Gram, Helm (Hammerhand), Fréalaf (Hildeson), Brytta (Léofa), Walda, Folca, Folcwine, Fengel, Thengel, Théoden (Ednew), Eomer (Eadig), Elfwine (the Fair)
2014
1. The Outlaws of Dorthonion
Barahir, Beren, Baragund, Belegund Hathaldir (the Young), Arthad, Urthel, Gorlim (the Unhappy), Gildor, Ragnor, Dagnir, Radhruin and Dairuin
Mithrandir, Olórin, Incánus, Tharkûn, Greyhame, the White, the Grey, Stormcrow, Lathspell (Ill-News), Grey Pilgrim, Grey Wanderer, Grey Fool, Grey Messenger, The White Rider, Bladorthin
2. The names, titles, and deeds that Bilbo claims for himself in his conversation with Smaug
I come from under the hill, and under hills and over the hills my paths led. And through the air; He that walks unseen; The clue-finder; The web-cutter; The stinging fly; Chosen for the lucky number; He that buries his friends alive and drowns them and draws them alive again from the water; I came from the end of a bag, but no bag went over me; The friend of bears; The guest of eagles; Ringwinner; Luckwearer; Barrel-rider
2. Names of Men in the Silmarillion chapter "Of Men"
Apanónar (the After-born), Atani (the Second People), Hildor (the Followers), the Children of the Sun, the Heavy-Handed, the Night-Fearers, the Inscrutable, the Strangers, Engwar (the Sickly), Firimar (the Mortals), the Usurpers, the Self-cursed, the Younger Children of Ilúvatar