I understood the gist of what she was saying on first readthrough, re-reading it made everything clear, and yeah she's talking in third-person and also using a nickname for Tino.
Basically Liz took part in a campaign, rushed back using her super-speed to receive praise from MC, noticed MC was gone and deduced he was going to save Tino (which pissed her off because she thinks Tino being too weak means she has failed as a teacher in the eyes of MC and because she thinks it makes Tino a bother for MC and thus herself a bother to him), so she's pissed when she meets them and antagonizes Tino and her party for being too weak but MC praises Tino (and goes around the question of him giving her the quest in the first place) but Liz's absurd power means huge feats for normal people seem insignificant so she was ticked off when MC mentions that the party only took down one werewolf when working together.
Liz is a huge simp, infatuated with a lazy sack of shit who is incapable of saying no and instead weasels and slithers his way through life by perpetuating a persona of power while in actuality being powerless, and who heaves his own work onto others... She cute though so she alright even if there is about as much brainmush inside her head as MC's...