Dear F.:
All feelings aside, try to separate facts from cockiness. A big factor would be whether she has 'been there, done that', namely if she has or had a boy at that age and knows the stages you may be new to. Is she giving you a heads up on what to expect in the next stage of development? Is she telling you when the next dentist or pediatrician visit is due? Those are things she can tell you on an informational basis, ideally without mocking or hard feelings. Or is she just spewing her unfounded opinions on how to raise a child in general? That you don't have to take.
If you react harshly to her no matter what, you may be missing important information for the well-being of your child. I would only react harshly in cases where it's none of her business what you do to raise him.
As far as 'play the role of being my sons mother', she actually WILL play that role, like it or not (assuming they are serious about being together). At this stage you may say that they are not married, so she is NOT taking on that role. However, if it is apparent that they head that way, be glad she takes on that role. The alternative is that she would ignore your son in her family, and that would hurt him.
You may want to talk to her privately and clarify the boundaries. When I was a step-dad for eight years, my daughter called me 'W.' and not 'dad'. I think that is reasonable, because everyone has one mom and one dad. It does not take away from the bond you can have as a 'step'.
If you let her know in a nice way what bothers you and what is OK with you, everybody wins. You cannot influence which life partner your ex chooses. From what you wrote, it could be a lot worse... You don't have to be friends, but you should find and agree upon common grounds to keep up a level of respect. After all, you want your son to be respectful as he grows up.
My 2 cents,
W.