Hi OP,
-I use white noise apps for my baby all the time, most nights, always in the car and about half of all naps, at the highest level on my iPhone so pretty loud and he is fine. I like you worried about it being too loud and making him deaf or something but he's fine, and I have it on a timer now so it fades out a bit.
-Babies do flap hands and scratch things. Hand flapping is partly learning to move her arms, partly learning space awareness and partly self soothing. The scratching is her trying to touch things, she hasn't got the dexterity to gently stroke something every time just yet.
-Losing sounds are so normal, and so is your worry. Babies learn something, file that job away in their brains and move in to the next thing if they don't Immediately need the learned task, that's ok. It's your job to care about her, but step back and breathe. She smiles, she laughs, she looks all around? She's doing perfectly.
-Staring at your armpit is fine, she's just zoning out while she has a nice drink, absolutely fine.
-She is quietly observing the huge amazing world around her. Her eyesight is almost fully developed now, so she will be able to see across rooms, which she wouldn't have been able to do before. Incredible! Like us being able to see to the end of the road.
-I would honestly say that he head turning with sound and sight maybe points to her being overwhelmed. Try talking softly, tv off, hold her hands in yours and being so so gentle and calm and slow. Don't let anyone get all in her face, or do loud voices around her, she might just be really sensitive. Try wearing her in a sling? I wore my DD in a stretchy wrap, by Moby. She could hear my heart beat, have the warmth of my body, and we could be together without saying anything. I also found if she was fussy getting on and doing the housework soothed her and she'd sleep for a lot longer. Plus I could tuck her head into the side and she would be swaddled up and feel secure.
Sorry for the long post, feel free to PM
You're doing a great job.