The Conservative movement, to my knowledge, didn’t mess around too much with Nusach Ashkenaz (which is what their siddur is based on). Traditional nusach hatefillah is something that they actually retained more than many Orthodox, since they actually invest in training qualified cantors.
I don’t know of any synagogue ever to do havdalah on Shabbat morning. Maybe you were watching an instructional video taped outside of Shabbat? The movement has a teshuva where they don’t allow recording to take place on Shabbat.