I'm a 21M she's a 21F. In the span of a month, we've been on 3 dates:

First date: Waterfront park, enjoyed nature and got to know each other; Got rained out then she offered to go back to her place to dry up so we played some video games and made out

Second date: She had work late so she came over to my place and I cooked dinner and she ended up spending the night, did everything sexually except going all the way with penetration (she said she wanted to wait a little longer)

Third date: We go to a decently nice restaurant, share a bottle of wine, was going to go to the museum after but it got too late. She told me what she was looking for in a boyfriend and that she wanted to "take things slow" and told me about walking into her ex cheating on her 8 months ago (last time she has dated), I went back to her place and met her roommate and we played cards

The morning after she spent the night her mom called her asking about how our date went (come to find out she has shown pictures of me to her mom and talked about me) and at the end of the third date she was hesitant to invite me in to meet her roommate/best friend because she said that's a big step and when things are getting serious... But I ended up meeting her roommate anyway

Our communication dynamic is unfamiliar to me, we rarely text/snapchat between dates and after our third date she went back home for a week vacation to be with her friends/family and we haven't talked for 3 days. I text her 2 days ago saying I hope she's having fun back home with her family hoping to see how she has been but I never got a reply. On our date she tells me she "likes to be in the present" and doesn't like social media much, so I guess I shouldn't take it personally if she doesn't hit me up? But she still occasionally posts on Instagram & Snapchat even though we haven't talked since she got back home...

tl;dr - 3 successful dates, but she is very hesitant to talk about her feelings and her lack of communication and investment makes me question her interest although she did take some big steps with me and told her family/close friends about me, unsure how to take things from here. If she tells me she wants to "take things slow" and tells me what she wants in a boyfriend, she obviously wants me right? How can I make sure I give her what she wants and we both find happiness together?