To (somewhat) answer your questions in order;
It's unknown who injected Murdoch, but I believe it may have been Hannah Beaumont, as she was the one to also murder Jacob Oliver. If you mean the injection that brought him to life, it's Russell who administered it.
Murdoch ended up in the tub as he fell in after being injected.
I don't quite understand what you mean by "talking to himself at the table" since he never did talk to himself. In the scene, he sees Lillian by herself packing up some cards, leaving one. She is then replaced by another Murdoch while the "ghost" of his real self watches. There is no other interaction.
The girl, Lillian, was injected with adrenaline instead of caffeine, which caused her heart to accelerate too fast until it stopped. With Murdoch, however, it was necessary since he'd drowned and needed to be brought back to life fast. (I hope that makes sense)