Transmission trouble, and filing a claim with my warranty company

I think my transmission is starting to fail:

If I floor it while the car is already moving (with RPMs greater than 1.5K or so), then everything is fine.
If I accelerate moderately or heavy from a standing stop, either in first gear or in 2nd with the manual button pushed, the engine revs up a little and the car feels like it's sorta connected to the power then the torque converter lurches or whatever and the car will go (and peel out if roads are wet)
If I start from the top of a hill, and put it into 1st and just let it coast down the hill, I have no engine braking at all. I could be coasting 30 mph in 1st gear, with the engine idling.

I have called my warranty company to see what to do; they say to take it to a shop and have them call to get authorization or whatever. So I guess we'll see how well this warranty co. stacks up. And if anyone has any more ideas about the above (seems like the TC to me), please let me know! Thanks,