Hi there, thanks for the thorough feedback!
For the movement, unfortunately I'm not a skilled enough programmer to make Ban move anymore smoother... I think Renpy is just kinda limited in real time movement :x (if it helps though, he can be controlled with both mouse / keyboard WASD and arrow, and SHIFT can make him dash to make him move faster to evade monsters. Also, chance for escape is also still very high, so you are most likely successful if you decide to escape battle)
As for the battle, it makes sense to make it immediately available to at least level up a little. A possible tweak would be making Haves' initial strengthening potions immediately available (so, level 1-2 potions already available, which should strengthen player enough to beat the first 2-3 dungeons), and the more advanced potions (3-5) will be unlocked upon quest completion. That might be better? Implementing EXP system / courage-based increase at this point is a bit hard ^^;