Let me try to address these one by one.
What are the not to be missed food experiences?
Probably the most unique experiences are the ones related to Parmiggiano cheese. Cannot recommend one in particular, it's been too long for me.
Are food factory tours a must?
See above.
Is An Agritourismo tour a must ?
Not at all, they are places to stay, not to visit.
Same for art, motor valley and so on ?
Eh, this one is harder to answer... What interests you? Why are you going to that region in the first place?
How can we receive a tour of the Ferrari FACTORY, even though we don’t own a Ferrari?
I do not think you can, but the Ferrari museum (Maranello) is very good regardless! Or if you are more of a biker, then try the Ducati museum on the outskirts of Bologna.