Babies do sleep alot, just like human babies. However if she is 'sleeping' while you are talking to her I think she's not sleeping, she's just relaxed and content and is closing her eyes for a little rest. When I talked to my keet, she would tilt her head, close and open her eyes repeatedly but slowly, and grind her beak. Rocky does this too, but not nearly as much. He's much more active and hyper than she was, and can't seem to hold still for one second LOL unless of course he's cuddling.
I'm sorry I don't know exactly what you mean by this:
When she is fingered trained .. how long should I wait until I can felt her out in my room?
Because when she got out, she couldn't fly at all so she just walked on the floor.. is that ok?
You can leave the cage door open(as long as she's finger trained) as long as you're there to supervise. You'd be amazed the trouble they can get themselves into when you're gone for just a split second.
Going under the bed? I imagine its dusty, and it also would be hard and stressful to get her out from under there, so don't let her go under.