Some of that is right, some wrong, some very right, some very wrong...
Other than the lincon description, most of the rodeos seam right, same with misties...
Cork is when you are spinning on your natural axis, but that isn't verticle, it's somewhere between 0 and 90 degrees if zero is straight up and down.
D-spin is when that goes past 90 degrees.
Now, if you are only like 1-40 degrees off axis, you're looking not so great in that cork.. more like you screwed something up.
A flat spin, you are actually spinning on a different axis, instead of your axis going through the top of your head (this is if you are spinning like a pencil) and coming out your grundle, it's more like it's going through your waist right above your johnson and coming out your waist right above your crack....