Nagini being a Horcrux

This just always confuses me. How? Because we know she was made with the murder of Bertha Jorkins. Okay, but Voldemort was still in his mutant baby form then, so how was he able to work the magic for it? Seems like Wormtail would've had to do most of the work, but it seems unlikely you could murder and then use the murder that you committed to make a Horcrux for someone else, it seems like the magic would allow it to be only for the doer. Besides that I also feel like making a Horcrux would probably be too advanced for Wormtail.

Also, when Voldemort tried to kill Harry as a baby, intending to make another Horcrux then, I wonder what object would've been made a Horcrux then? I doubt something random from the Potter house, he probably would've had something with him.