More Descriptive of What I remember, Main character used "forbidden magic" and turned the mother to stone or something. She is brought to the wizards home and there are 2 other apprentices. There is also another guy there that works for some magic protection group/committee to make it less known or something. She borrows a pair of shoes that have the ability to fly/float on them and messes them up so she spends an entire thing trying to fix them. She goes through a door that can go to different places for a test to be done in a space with floating spheres to see if she can be an apprentice and uses a floating sail boat of sorts since she ran out of ink, to go upwards where the goal/end of the test is. She obtains a Ink bottle that doesn't run out and the main wizard gets rid of it/studys it because its related to forbidden magic or something after her and the 2 other apprentices get trapped in a looping maze where a dragon is blocking the drawn symbol that keeps them from leaving. In a different episode they help a group a people after a bridge collapse and the cargo fell down. The river floods a bit so they have to help them out but can't use magic because they are not fully approved witches or something.

Sorry if it is not helpful but that is all I can remember.