Okay dude, I haven't lived my life very long (only 30), and I've only been in a couple of serious relationships, but here's what I think of it all.
I became extremely upset, starting to cry like a baby.
I have been there before man. Don't ever do that again. Life is cruel, people will be cruel. This is a sign of weakness no one likes. It can't be helped, I know, your emotions are your emotions, but don't let this happen again with this girl.
The "atmosphere" was right, I mean you got the setting, the mood, etc right. The timing is wrong because she's not looking for this right now.
Hard to say. I know the answer you're looking for, as would I, is yes, she likes you, just wait for her. But I'm going to tell you I've been in your shoes before, and it has worked out once, and it has not worked out once. She shows signs of affection - holding hands, cuddling, etc. There's a very good indicator she likes you and she's just holding back for some particular reason. However, she could also just be lonely, or wants a replacement for her ex, or god knows what.
This is up to you. If being just her friend hurts you, and you see it hurting you long term, ask for space, or cut ties. If she's just comfortable with you as a friend, and you're heads over heel for her, one day she's going to break your fucking heart in pieces. If she's valuable to you as a friend, and you can see yourself moving on, then give up for now and stay as friends.
No, it's a sign of interest. Life is cruel, people are cruel. Sometimes unknowingly.
"that she doesn't find me sexually attractive" Pretty fucking bad sign that it's hopeless.
It seems to me that you're an emotional/physical cushion replacement for her ex.
The heart does what the heart wants... if you really want to chase her, go for it, just pull back a little bit. If you keep pouring out love and affection to her, she'll take that for granted and that's really going to friendzone you more at this point. I know there are stories where guys just brute force (pour out love and attention until the girl falls for them), but honestly that rarely happens. But tbh, it does seem a bit against your favour. If you think she's worth it as a friend, take some space away from her if you need it, otherwise just go on being friends.
Just take it as a life lesson if anything: life can be cruel. My ex-gf hugged me, kissed me, told me she loved me, then proceeded to dump me a few days later. People can be very very cruel. Just take the heartbreak, and strive to be a better person. You'll be fine man. Take care. :)