Urgent advise!

Me and my ex had broken up for 2 months now.
I have neglected her for the past 2 years during her pregnancy and birth of our son. Was not always there for her when she needed me most and got her into financial stress/continuous arguments and verbal violence.

There has been great improvements since the beginning till now with the break up. When we first broke up she told me to stay out of her life and we are just parents of our son and don’t intrude her life etc,told me to find a new girlfriend and a new life.
I think what triggered her aswell was us selling our house and she moved back home.

Now we are so called “friends” BUT she allows me keys to her parents house,sleeping on the same bed, kiss on the cheek/forehead every morning/night,goes out shopping/eating with me,no more mentioning of telling me to find a new life or stay away from her.

But she is still quite blunt on social media/messenger etc when we are not together.
Since the broke up I treat her like the queen/princess and make her hot drinks,house chores for the family,body massage everyday.
But she now pretty much takes it for granted.

Question is- how often should I communicate with her via messenger etc?
Besides improving on myself and the problems that caused the break up what else do you guys advise?
I am giving her space and freedom and don’t demand or question her life either but she tends to tell me her self.

Also she has been constantly saying I am scarred from relationships and don’t want to be in a relationship, she’s keeping the door open for me to win her heart back again but don’t know when or how it will be.

She's shut that door but leaves it open enough to get whatever she needs out of you. She feels you owe her so your time is currency and nothing more. What should you do? Move on. Pay your support for the kids, and do your visitations. Start fresh with someone else.