In the past I've used a radiused subway to turn the corner. It softens the corner due to there being more tile and fewer grout lines. For the base I'll use the inside or outside cove corner pieces to turn corners. Here's an example of a radiused subway for turning a corner:

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In your case it sounds like you want the outside corner quarter rounds to be black so they will almost frame the wall tiles, In that case, sure, you can simple have a vertical run of black outside corner quarter rounds to turn the corner for you.

Your questions:

1. Yes, you can do that.

2. I'd use true cove corner pieces on the cove to turn cove corners. Running quarter rounds to the floor and having the coves butt to each side of the quarter round? I don't see the profiles matching up at all.

3. See answer #2 above. If you run outside corner quarter rounds to the floor, the profile of the outside corner quarter round will not match the profile of the cove. So use cove corners for turning corners with the cove.

Thanks Mongoct! I really appreciate the help. I don't think the subway tile I'm using, Daltile, makes a radius subway tile to wrap around the corner, but let me know if that's wrong. I'm also told that Daltile doesn't make inside cove corners and those need to be mitered. I will plan to use an outside corner on the cove below the quarter round, though.