Several of the things scream ASD to me.
Of course it may just be that she has poor manners generally due to lack of boundaries. Or it may just be a one off incident of bad behaviour for other reasons.
Whatever it is I think it is absolutely essential you get over the feeling of embarrassment re telling the mum/dad exactly what happened.
All three of the reasons really require you say something to the parents so they can deal with it.
Walking into a bedroom when an adult is dressing is quite a risk to her. Picking up a newborn is quite a risk to the newborn. She has said a number of innapropriatr things which will affect her social life.
I feel like moaning on the internet is a bit crap unless it spurs you on to do the right thing and let the parents know, as school would if it had happened there. I also think you can't really complain about a child being rude about food and then call the child sweaty names on the internet. That's v hypocritical.
I understand that it is difficult, I recently had to tell my friend I was concerned about her little boy (5) as he had pestered me to take him to the toilet for a poo and wipe his bum for him while she was in the garden and when I hadn't seen him since he was a baby and that I felt this kind of thing could put him at risk (highly likely he is on the spectrum).
As a parent of a DD who is about to be diagnosed with ASD (all reports in and showing severe deficits) and whose school covered up everything that went on until she stopped going this academic year, I will say it is absolutely VITAL that other people who see behaviours when they have care NEED to tell the parents so that they can deal with it. Otherwise you get to 10 like my DD with huge anxiety, agoraphobia, no friends, no education and a shit tonne of maladaptive coping mechanisms that are really hard to shift.
Not saying she has ASD by a long shot, but behaviour like this should be reported to the parents by everyone who sees it so the parents get the full picture and are informed at the very least. It is the kindest thing you can do for the family.