Search Results: should i ask him out first move

Hi there!

Me [35M] work as administrative role in our department, which a new girl[23F], meantime she has her school holidays, began her part-time job just over summer.
Since we're working in a big department, but in separated areas, we're not bumping in each other every hour, maybe except during lunch break, coz we share same canteen. To me she's cute, I'm old.

First encounter
In the beginning of this week, she pops up in my office coz she had some problem with her profile account. So in order for her to show me, she had to logon from my computer, so I moved away a bit to give her space.
After she was done, I rolled back so could start a short troubleshoot on what was going on.
But I noticed something with her behavior.
She didn't back away when I started working (that's what people usually do?), I mean, my office is big and she had plenty of room to casually back off..
So she just stood there very, veery close, like we could with no problem play a game on my computer using same keyboard..
Short after she had to logon again, just to clarify, so I moved away again, but this time "not so far".. So I expected her to try to reach over from where she stood to my keyboard, or just move the keyboard to her so she could easier type.. But nope she went just in front of me and start typing.
Her current position; she could just turn around and sit in my lap... WTF?

And then everything seems good, so she left back to her work.

Second encounter - Coffe machine
We got two machines; I was waiting for mine to be ready and she came and ordered hers.
So I had to ask her if everything is going well now since my high leveled supportexpertise saved her day, and gave her a smirk.
She laughed (giggled?) a bit and said yes, and looked on me very fast and then looked away.
Then I noticed she was super red in her face, blushing (?).. She didn't blush when she was in my office?

Am I overanalyzing things?
Coz now I instead confusing myself and need help.

So my old partner and I were both married when we worked together and we became friends for the year we worked together but as my relationship failed again I would still talk to my friend that used to work with me because she messages me almost everyday and asks how I am and so one day she told me how her husband hit her and I already knew he was always an asshole to her and I told her that I really liked her and she said she is a married woman and I am her best friend.
One day I told her that I was confident we will be together sometime when she was fighting with him and she said come to the city and get you a place and a car and work on yourself bro and their is a first time for everything, so I moved up their closer to my work place.
A couple months after living here my ex expresses that she wants to come be with me after her boyfriend beat her up and is locked up but I say no and she meets up with my friends husband and tells him all kinds of lies and my friend left him but then got back together with him and blocked me for a few months.
Out of nowhere I get a message from her saying she left her husband for good this time and I say sorry.
After she told me that wh started talking again and she would start half the time by messaging me how was I doing or something and after a month I started hitting on her and she would say we need to hang out.
I would hit on her a d compliment her and she seemed to like it because one day I said I'll stop saying that stuff tobyou all the time about her bing really pretty and stuf like that and she told me no you dont to stop and so I said I see thay as an invitation to turn it up on the hitting on her and she said yeah I can.
She would video call me when she would drink but all the sudden she went cold and barely answer texts after her ex put his hands on her but never said anything else and is different now
What should I do?