If I use Heavy armor and cast an Oakflesh or other armor spell, will they stack on each other?

Yes. The only thing that won't stack will be the Alteration "Mage Armour" perks, for those to work you can only wear clothing. But for the basic spell, with no perks, they stack.

Easy to test it, put on a piece of armour and cast oakflesh, if your armour value goes up then it stacks.

Yes, however, there are some alteration perks that massively boost the effectiveness of those spells if you are not wearing any armor.

As far as I can tell, the answer is yes, but keep in mind that the Alteration spells have perks that, IIRC, double their strength if you are not wearing armor. So, you will get some benefit from the shield spells, but not the full benefit. Still, armor plus partial strength shield spell is better than just armor. (Unless you've hit the cap, at which point additional armor rating doesn't help much).

yes

This is the way its works, you can definitely use it with armor if you wish to use it. I am going to make one who stacks it with armor and one not use armor with it at all.