I just replaced my heater core in mine, and let me tell you it was a job. Nothing for the faint at heart. Getting to that HVAC unit is a pain. But half way into it I was beginning to second guess why I tackled the job, but after I got it done and realized the cost savings, I was glad I did it. Plus I knew it was done right.
As for you specific problem, I don't know why it would be doing that. Do you have Dual Zone Control?? Anyway I looked around my unit when I took it out, just out of curiosity to see how everything worked. The flaps are controlled with a armature that's driven by two gears. One gear (the driven gear) is attached to the armature, and the drive gear is a spiral gear attached to the motor shaft. Maybe the drive gear attached to the motor is spinning on the shaft. Don't know just throwing something out there for you. As far as the water sound your hearing, I have no idea. Hopefully your core isn't busted either, but you would know by the antifreeze running out into your floor board. There is an over flow spout on that HVAC unit to allow antifreeze to run out if the core does bust. The spout is on the lower passenger firewall in your engine bay. It may be possible to fish a string down in it, and pull it out and see if its wet. If so, then time for a new core.
If you feel like tackling the job yourself, just post back in this thread and I'll help you out if you get hung up on something. I'm only 2 weeks removed from doing mine, and it's still kinda fresh in my head. Just remember, if it don't come out willing, don't force it. There is a lot of hidden bolts and screws. Post back in here and I will guide you. Also AIR RAM also knows how to do this, he gave me a good heads up to get started, and some help along the way. Here is my original post.
If you don't have to change out the heater core, then you won't have to discharge your AC. But you won't know till you crack into it I guess.
At any rate everything I typed my not apply to you, especcially if you have dual zone, but I can help you get to the HVAC unit if needed