Cancer women, are they private or secrative?

This question is for all who have either dated a cancer woman or know one.

I'm dating this Cancer Girl, 4th Juy born. We been going out and having fun. We also enjoy staying indoors and have great physical chemistry. But there 3 very peculiar behaviors;

1. I have never been invited to her. It's always my place. And one day I asked her, and she just asked her in jest, as to how come she has never asked me to beg place. The response was something very unexpected, "you know how I feel, one day I'll invite you". Well apparently, that day has not come.

2. Every time we are together, I notice that her phone is face down. She gets a frequent texts, and has fairly active social life. She broke up with her last BF a couple of months ago. They had known each other for some years.

I'm not a insecure man, but just being cautious.

I don't do rebounds and don't want to be one. We met on a dating website, and we been dating for over a month.

3. I have read that Cancer are loyal, but loyalty is also a personal trait. Cancer are layered and nobody can really know what they are thinking. What, I find surprising is that, during this initial courtship time of excitement, she spends Friday evenings with me and then wants to head back to her place on Saturday. I know she is busy and pretext is usually work, but then some friends of her make plans and she is out. In all honestly, she does tell me that, but I find it Weird and tricky.

Without offending or disrespecting should I approach and ask her question or be patient.

Any thoughts Cancer ladies is highly appreciated.