Regarding the tuning, keep in mind that your environment can affect you tuning. When I practice at home, my mouthpiece is close to the end of the cork. When I play out somewhere, I frequently have to have my mouthpiece on halfway or slightly farther out. The acoustics of the room you're playing in have a lot to do with it. Just because you're in tune with your mouthpiece at a certain spot at home, it doesn't guarantee it's still going to be in tune when you go somewhere else.