I have never installed a Y-Y either. Never even seen one in fact. As iaov pointed out, harmonics are a big issue on this setup (especially the third harmonic) and other less troublesome transformers will do the same thing, so Y-Y is uncommon.
Now to your questions (as best I can):
1. If the transformer is Y-Y it needs fed with Y and will therefore have 3 phase conductors plus a neutral.
2. You just need to change the picture in your head. A three phase transformer is nothing but 3 single phase transformers. Delta and wye are just a matter of how the three are connected together. You have three independantly operating transformers. If you give two of them no power, those two will be off.
3. Delta-Delta is the only type recognized as being protected by the primary OCP. Delta-Y, Y-Delta, and Y-Y all must be protected on the secondary side. I can't explain why this is, so I have now pulled out my old college textbook. After choking on the dust, I see that delta-delta is the most stable type while Y-Y is the most unstable. Y-delta and delta-Y fall somewhere in between. I hypothesize that delta-delta is permitted because of the stability of the transformer while the others are not because they are less stable. Perhaps someone older and wiser can comment on this.
I'll not call the NEC wrong on this issue or any other.

The end goal is to keep people safe and I say better safe than sorry. Err on the side of caution.