Why'd she all of a sudden kill the family whose basement she was buried in?

They dug her up, which in effect "activated" her, or made them accessible to her (although speculation, perhaps being buried prevented her from projecting her illusion with an effective potency). The healing that had occurred to her externally happened as the result of their deaths. She basically takes the life from those she hurts/kills and heals herself with them. Presumably with enough life force she could fully awaken.

Why didn't the girlfriend say anything? Why was she there in the first place?

She probably did say something. But Jane Doe was masking reality and replacing it with a shared delusion/illusion for the Tildens. Notice the body with the bell never actually got up and moved around we find out at the end. It was all in their heads. The radio changing channels didn't actually happened, there was never actually a storm, the "old oak" never actually feel on the doors. All an illusion. What was real was everything related to the autopsy. The girlfriend was there because Austin had told her to come back at 11pm.

What was the point in her regenerating and transferring everything to the dad if she was still going to be a murdering witch?

She transferred nothing to the dad. She transferred "energy" or life force, or whatever other term may be deemed relevant, from the dad to herself to heal her wounds, as well as the damage they'd done to her during the autopsy. As she took Tommy Hilden's energy to heal herself it caused her injuries and damage to be replicated in him. Unfortunately for Austin and Officer Cole (the guy driving her at the end) it wasn't enough and she needed more. Who knows how many it'll take before she's fully alive again. She did just have her heart and some organs removed that'll have to regenerated, after all.

Have to agree with you. This movie was a very pleasant surprise! I like horror flicks that take their time and breath because it infuses it with a stronger sense of realism and dread.