When I lay down my breasts fall all the way to the sides of my body. Is this normal? Who's responsible for fixing it? (Photo)

I am sorry to hear about the problem you are experiencing after breast augmentation/lifting surgery. Based on your description and pictures, it seems like you are experiencing a lateral breast implant displacement problem.
Generally, the lateral breast implant displacement can be corrected using an internal suture technique, decreasing the size of the pockets and moving the implants toward the midline. Doing so will prevent the breast implants from migrating to the sides when you lie down and will help centralize the position on the breast mounds. In my practice, this repair is done with a 2 layered suture technique. The use of acellular dermal matrix is an option ( although not usually necessary) especially if significant implant rippling/palpability is present.
I hope this (and the attached link, dedicated to this type of revisionary breast surgery) helps.  Best wishes.

It's normal for breasts to move and be a little differ left to right. Any additional surgery would carry risks and not be recommended. Close follow up with your plastic surgeon is recommended.

Yes, this is normal. Sleeping on your back and with a bra is a good idea for keeping your breasts looking well.