Level System:
Each pokemon you cause to "faint" will give you 1 exp for each level of that pokemon for each member of the group.
The required EXP to gain a level is by this formula (rounded down). X=your current level.
0.1X²+10x.
Leveling up not heal you fully.
Traveling System:
Using the map system each team and individual can only travel along one path from one location to another once every 8 real life hours.