1. Yes - they have polycarbonate lenses. No special case came with them - I just chose the standard soft pouch, although it is overkill. I could easily find something smaller if I looked around.

2. Yes - they are BUTT Ugly! But - I bought them to wear inside a gas mask, so BUTT UGLY is a relative term when you're looking like an Ant-Man from the center of the moon.

3. I don't remember the price, but as I recall it wasn't any worse than normal plastic lenses.

4. I did not buy them for use as a scuba mask. They just give me the ability to see as well under water as someone with "normal" vision would have. When you have trouble seeing the BIG characters on the eye chart, you need all the help you can get. You don't want to grab the wrong bikini - you might get slapped.