First off you need to evaluate all medical reasons why she acts like this such as PPD. Depression would explain a lot.

After this is ruled out you can try couples counseling and sex counseling.

Because of you mentioning her being on her phone alot I also have to mention cheating as a possibility. If she shuts down the two first suggestions cheating starts becoming a more likely option. I would start snooping if it reaches this point.

Make sure that she understands that your relationship is on the line if she doesn't agree to the first two suggestions.

Too soon as people say, if you have no other reason for moving in together just wait at least until you've been together for a year. Also where I'm from you can rent out your apartment second hand for up to two years while doing trial living with a partner. Not sure anything similar exists for you.

This just seems wierd, most people would save their porn as favorites on said porn pages and not in notes.

That said porn is fantasy and not reality. Don't get in your own head over this.