Cake. It's even in the name of it. xD

Mincemeat is spiced, dried fruit--although originally it always had meat.  So it would be pie either way.

Yes.  The primary ingredient is cream cheese.  

I would have to say pie, because cake generally has frosting and is lighter and fluffier. Cheesecake also has a crust, which cake does not. I mean, no one would call pumpkin pie a cake, and they're extremely similar.

Cake, it's a cake.

A pie crust is universally either pastry or bready. The cheesecake base is never either of these. It is a crumbed biscuit (cookie for Americans) base. Since a biscuit (cookie) is basically a hard, flat cake a cheesecake is basically like a thin, hard crumbled cake with an extremely thick and dense layer of a cream cheese icing.

It has the appearance of a pie, especially when baked, but the content is pure cake.

This did not make sense at all.

The pastry itself IS a cake. Just because pies have pastry that does not make them anything like cake as you are implying to happen with cheesecakes. Cake+large filling = pie. Cheesecakes are pie, and have cake on the bottom and sides like every other pie.

No, pastry is not a cake. 

No idea but I knpw it's not very tasty.

And biscuit is? Ok, keep telling yourself that, good luck.

Cheesecakes in the USA typically have a crumbled graham cracker crust. For those of you not familiar with American graham crackers, they generally are flavored with honey and/or cinnamon, and are pretty sweet. They look like crackers, but, IMHO they're closer to cookies than crackers, in the American sense.