It should be fixable by weight painting… which is a bit of an art in itself. Auto-weights only get you a good starting point (about 70% of the way and generally good enough for cartoonish-renders).
It is important though that when placing the rigify rig that you get your breast and shoulder bones in their correct positions as this will make later weight painting easier to do.
Your topology is pretty high-poly already… don’t think you’ll need to tweak much there.
Weight painting (which isn’t really covered in-depth for rigging in this course) takes some getting used to but will get you 90% of the way… which is 100% good enough for most game rigs and NPR animations. If you’re wanting to do ultra-realistic animation, then you’ll need to spend lots more effort adding shape keys to deal with bone deformations in extreme cases.
Yes, do this.
Hope that helps.