If I play an elf, and I increase in level and take the level benefit instead of the spell inventory slot, does my mentor still teach me a new spell? Thus, regardless of choice, I always am learning new spells? I just don’t get the next level of spells?
You can always try to convince your mentor to teach you a new spell, but your mentor will only do it automatically and without something in return when you choose a spell as a level benefit.
Also, you do not gain a new spell memorisation slot.