I personally have never ordered one off the menu, their staff is more then willing to make your experience one that you would be happy to share with others so that being said. I feel they would enjoy crafting your drink of choice. Who knows maybe they add it to their menu!

Yes!

There is a pay lot a block or two away.

Email works too.

No dress code. It's a fairly nice place though, I usually wear business casual

They didn't have the night I was there but there is a small stage with a piano. I'm pretty sure I saw a picture with a performer on stage, somewhere in their reviews.

Yes

Hours should be online. There is a very cool private secret room accessible through the phone booth!

I would maybe make arrangements with them ahead of time. Sometimes places/bouncers get worked up over the paper licence. Big difference if they're expecting you vs you walk in on a busy night.

Every second Thursday there is gypsy jazz: Parisota Hot Club. Truly incredible!