I'm looking for a manga about a strong girl with strong magic.

• girl saves another girl in a tavern from some ruffians, then talks to a (beautiful) man who tells hee that it was a bad idea

• she leaves her family to go to an academy where the first test is to strike (with a wooden sword) a dummy 100,000 time. There was a weak boy (blonde rich boy) who passed as well and thanked (praised) her after words.

• she goes through tests like how many beads they can thread (they annoy a fuy behind them because they were talking and "distracting him"? where the threaded beads are then weighed and strenth where she and a boy who is unable to controll his magic destroy the punching machine.

• she goes to a battle arena where she has to fight other participants. They attack her because they think shes weak beacuse she's a girl. She pairs up with a really strong guy and pass. They end up becoming friends.

• she goes on a quest through a forest with lots of beasts and runs into merchants(?). One was a little boy who could summon water(?) and earth spirts from the ground.

• she remindes the boy of his elf(?) mother who was eaten my a beast (monster) in front of him while they were running away and his father was out. (elfs atract beasts).

• they were attacked by a beast and the girl saves the little boy and ends up breacking her arms. The boy summons a water(?) fish spirit who heals her arms (mostly).

• a guy from her past comes into her tent while she's sleeping and gives her a magic potion(?) that can heal any wound.

• once she gets back to the academy she is doesnt participate in a school duel/battle as she didn't dint the medicine/potion and her arm is still broken. [m]