I spontaneously messaged an old classmate of mine and now have no idea how to move the conversation forward. I ask questions and she answers them some time later (doesn't feel like she is disinterested). How to move the chat forward to get to know more about her
Start talking about something you're interested/know/have done and she will relate and talk about her. Conversations ser all about talking and hearing
Ask her out
Text her that you are gonna call her, and then call her. You'll feel much better after.