Wrt the newborn baby crying, could it be cats? The sound of cats at night can REALLY sound like a newborn baby crying. The sound really unnerved me the first few times I heard it until I realised what it was.
The sleep paralysis can be terrifying and seem very real. I've had a far shadow "man" stand at the bottom of my bed, over me, get in bed with me, pin me to the bed by sitting on my back, breathe menacingly only my face, move my blankets so I can feel the air current around my feet, the sound of it walking up my stairs and into my room, and all the time, I cannot move at all.
The way it's described is that your body goes into paralysis to stop you from acting out your dreams, and your brain and body should fall asleep together. If your body starts to fall asleep more quickly than your brain, you will normally get a hypnic jerk (you jump, which jolts you awake) but if this doesn't happen and your body goes into paralysis first, your brain can play tricks with you so you see/hear things that aren't there.
I get some form of it most nights, but probably once every month or two months I'll get a really bad one, that even though I know it's not real, it really shakes me up. If you don't understand it and understand how the brain/body sleep mechanism works, then it can seem like there's something paranormal going on, but if you read up on it it really does reassure you. I used to think it was ghosts I was seeing, but now I don't believe in ghosts.