You should get experience for every fight you do, whether you initiate it or not, but it doesn't seem like you do.
It also appears that you receive no exp. from tournaments, but I can't be 100% sure on that one yet.
My best fighter is only 1/3 the way thru lvl 6, so the more your lil sis levels up, the more you level up, the more you help me to level up.
We all need to get more pupils, other wise we won't be able to start a clan until near the end of the month.