Is it permissible to eat badger meat and to seek healing with its fat as an ointment?

Eating badger is forbidden because it is a beast of prey that hunts with its fangs, and it falls under the general prohibition of eating any fanged beast of prey. It is also considered repulsive.

As for treating oneself with its fat by anointing with it, if its benefit is proven, and it is not of the same category as forbidden food, but rather it is a matter of being soiled with impurity out of necessity, while being careful to wash it off before performing prayer, then this is permissible.