Questions: Girl's Behavior

I finally met a woman who makes me feel comfortable and had an instant connection with. But from the start, she has said I am not the type of man she wants, although the lines have blurred at times with things she has asked. I didn't want to hear it because I like her so much, but I figured I'd rather have her as a friend than not at all because we get on so well.

Things started slow but grew to where we were talking for hours every day. This is not like me, I don't talk to anyone, but with her it feels natural. even the pauses felt comfortable. I have never got on with anyone like her. I know it's not alpha, but I like the support we give each other.

Our relationship has been purely phone-based for a year because we live apart and neither of us tried to change that until a couple of weeks ago.
The day started great, she text me first, and later she called. It was our best chat yet. 2 hours into the call and I mentioned I was going to be in her town soon, so I suggested we should hang out or get lunch. She reacted badly and we had our first disagreement. She said meeting once would change nothing. The call ended awkwardly. A couple of days later she called me, and I apologised for putting her on the spot, she said I upset her but she upset herself too. I asked if we were OK and she said yes. That call was short but still awkward. We went from talking every day to nothing for 2 weeks which has made me soo down because I felt like I lost my best friend, but yesterday she called me out the blue and was talking like she used to. she sent a couple of texts which had her playfulness back too. The calls were short as I was at work and couldn't talk, but I text her at the end of the day and she didn't respond. I text her again today and she replied with a single word and a smiley emoji

What does she want?
Why react negatively to an innocent invite?
Is the friendship over?
Why start communicating again, but later fail to reply to my texts?
How should I move forward?

I don't know what it is, if its my face or something but babies seem to always smile at me. sometimes im not even trying to get them to smile ether im just kinda minding my own business then the baby's look over at me and smiles lol. i've even managed to calm down a few crying babies when nothing else worked at times.

do babies love you too?

I’ll just make a list:

* Smiles and waves first whenever she sees you and looks down
* Looks at you from afar but often I just catch her looking away or sits somewhere she can see you
* Chatty and bubbly and asking questions one day and quiet and not very ‘into the conversation’ the next? Like short answers, quiet etc. Also fiddling with stuff like a phone but not actually using it. Just tapping some buttons quickly and putting it down. This was when she was quiet.
* Sometimes only does a slight smile, rather than full-on belly laughing, when telling a joke or saying something in a humorous way
* Shows you photos of stuff on their phone
* Plays with hair and then turns and looks right at you (knew I was in the room beforehand)
* Tells you about some of their likes and dislikes (music, favourite weather, pets, future plans)
* Open body language - feet pointing towards me, arms aren’t folded but by her sides, sits straight
* More confident when with friends
* When talking, makes eye contact for a few seconds and then looks down or to the side whist talking and smiling a bit
* Always facing you (whole body and feet) when talking and standing

Bonus one:
* Tried to talk to me first many times in the past (but I didn’t pay much notice at the time as I was occupied with so much stuff at the time) A few of those past interactions she was fine talking and others she was quiet.

^ This above one makes me think she’s liked me for a while and usually, I’d imagine a introverted girl or a shy girl wouldn’t try to get a guys attention anymore than twice before giving up. She’s tried like… 6 times since October last year.

FYI - I’ve already gotten past the approach barrier and we’ve spoken a few times recently for about 25 minutes each time.

Any input is welcome and thank you in advance girls and guys!