Charcter physics and groundedness

Is there a detailed documentation on how charcters work regarding physics? I have cheked the charcter controlle page, but it seem insuficient to me:

I know they are not affected by phisics like rigid bodies because it would have undesirable consequences, but I need to create a jumping/falling sliding system that take sinto consideration a charcter´s inertia( his jump is affected by his previous speed, can´t control hat charcter mid-ari, exept for turning, slide is base don previosu speed, and so on)

My character only fall when he is not walking, If he walks off aledge he keeps going, but when I stop he fall normally, yet I can´t seem to have gravity work when heis jumping.

Aditionally mwhenever he is not standing still Unity says the charcter is not grounded, even though there is no height variation between his idle and walking state.

Thank you for your time.