Sorry, I have no BYOB experience in New York, but my Chicago experience would be that

1. There is no tax on a corkage fee

2. 20% is fine (and you tip on the pre-tax amount). Depending upon the size of your party (often 6 or more), they may add an 18% or so gratuity. However, if they haven't discussed it with you, they probably don't do this. But you should ask to be sure.

3. The corkage fee in Chicago is $20 - $25 if there is a fee. Some restaurants don't charge a corkage fee at all. I understand that you would have to search far and wide in NY for a place that doesn't have a fee, however.

I'm sure you'll get some NYC input.