Is there a human baby carrying and breastfeeding reflex? Because like I've noticed if I get an object around the size of a baby I automatically hold it like I'm holding and breastfeeding a baby.

Probably true for all of us. I can't sleep without my "Guling", here's an example:

If I don't have one away from home I either make one with the duvet or use a pillow!

oo. I hold my cat like that and never paid it attention    It's more like cradling it, rather than breastfeeding .. eww

for the "guling"..
I've trained myself to sleep without holding something but it took me a few years. Up until I was 17 I couldn't sleep unless I was holding a stuffed animal/pillow