Sure thing

Falling in love: she'd probably be relatively outgoing to whoever she falls in love with. Probably approach him and initiate the friendship, and do her best to get better accquainted and move things along.
Getting injured: depends on what else is factored into the situation. If she were in enemy territory, she'd most likely try to lay low and wait until it's safe to move, and tend to her injury to the best of her ability meanwhile. If she were around friendly creatures, she'd ask for help.
Someone dying: Provided it's someone she likes, she'd probably weep at their side and then respectfully move their body somewhere appropriate.
Annoying or badmouthing: She'd probably shrug it off to a point, but if they persist long enough she'll attack.