Ceiling Fan Replacement - Wiring Issue
Odd that you said you had a white wire that was hot. Both white wires should be neutral and have no voltage. Seems to me wires would go like this: connect all black wires together. That will run hot all the time to the fan as well as sending power downstream.   Next tie all white wires together. That will provide neutral to the fan as well as pass neutral downstream. Ideally there would be a bare copper wire coming from the hot side and another to continue downstream. The red to blue should switch the light, providing that blue is the correct one for the light.