Nah. Fascism only tolerates one power, that being itself. It can emerge from either the state or corporate side, and necessarily subsumes or destroys the other, just as it subsumes or destroys unions, families, friend networks, communications, and anything else that can establish power. That doesn't mean the merger of two of them is the defining feature.
No. Power can be delegated. I'd say capitalism puts ultimate power on the government who delegates power to holders of capital. (If that stops, it's not capitalism any more)
Corporations generally tend to only tolerate the state to the extent that guns or courts mandate that they must. How many billions of corporate dollars have gone to fund campaigns to deregulate, to skirt authority, to do whatever is necessary to make sure profits go up?