It sounds like either the shoes are not the right shape or fit, or there is a pressure point on your big toe. Or maybe you put too much weight on your big toe rather than spreading the weight across all of your toes?

Usually yes, but it should really be more of an uncomfortable feeling rather than actual pain. If you are used to climbing shoes, it may be fine, if not, you get used to it pretty quickly, assuming you didnt size down too much.

I understand the concept of soft grades, but, when it gets to the point where the grades are so soft that a v5 is actually a v3, shouldn't they just give it a v3-v4 grade instead of just calling it a soft v5?

All of the boulders in my gym are actually around 2 grades below their given grade, I don't understand why they give them the higher grades and not the actual lower grades. Is there a reason for it?