Why would a "corp" need Class 3 firearms?
It's not really a matter of why, simply that the law allows that method of ownership/possession. That is, I don't believe you have to come up with a reason in order to set up a corporation to own/possess Class 3 firearms, you just need to satisfy the legal requirements set forth in the law.
As is true in any state, you must satisfy both state and federal laws. The fact that something is legal at the federal level does not have any bearing on whether it's legal at the state level, and vice versa.
If your state's laws set forth additional requirements for owning NFA items, over and above those stated in federal law, then you will have to abide by your state's requirements in addition to the federal requirements.