She is finally opening up !! I would not change a thing. Your progress is natural, it will grow as you spend time together. Tad, you do not need a title ("dating, relationship"). In my opinion, you had plenty of "dates". why rush things!
I can see your respect toward her. I can she her lead. I also see that you are afraid of bringing her into your part of life. Her place, her invite. Because of the many declines on her part, your are reluctant to ask again. How about rephrasing your invites? You have a perfect opportunity right at this moment. " Would you like to decorate my place with me? ". Instead of " would you go on a date with me?; How about: " Would you like to spend time with me? or go for a walk or do something together?"
Do not worry about the imaginary line between friendship and relationship. From your words, if the moment of a kiss or a hug present itself, YOU WILL KNOW, you will feel it from you and from her. for now, enjoy what you have!
I would not change a thing. Your progress is natural, it will grow as you spend time together. Tad, you do not need a title ("dating, relationship"). In my opinion, you had plenty of "dates". why rush things!