When using ability checks I often think about whether knowledge of something fits into one of the skills. 

Is it a nature-, religion- or just a plain intelligence check to recall knowledge about creatures of other planes or undead?
When talking about laws, what kind of check would it be? Probably plain intelligence.

The problem occurs when one of the characters is a demon hunter or a lawyer by background. There is as far as I can see no written rule which lets you get proficiency in such checks.

**Do you have experience in adding own skills and let players get proficiency in them? Are there problems coming with it?**

When thinking about a demon hunter and giving him the "demon lore" skill (or comparable) it would also give him proficiency for checks to recognize demons and recall their abilities, but might be to a too edge case skill. Giving him something like "Monster/Creature Lore" it might be too widespread for the character.