What does is mean to worship, not at a mountain/place, but in spirit and in truth? Does it mean we have to be “spirit filled” in order to be the worshippers the Father seeks? Who in their right mind worships their father anyway?

I think that worship in spirit and truth means to do what Jesus did. Live in love and grace, and share it with others. All that is required is to merely be ourselves, one with God and spirit, and by extension, one with all. When we sing of our joy over this, know He is singing it with us. Worship? Not so much. Oneness and joining in the divine dance.  That is how I see it.