It is not appropriate to have an ex gf spend the night in the house you two live in. It only leads to trouble. Generally, I do not contact my ex girlfriends. If my ex emails me once every 2 months, that is fine. If my ex emails me 4 times a week, I tell my current gf so I don't appear to be hiding anything. If my current gf objects, I tell my ex to stop emailing me.
Your bf should not be doing anything that makes you uncomfortable, or appears to threaten the relationship (within reason).
These are just the limits I go by.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
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