I also just started rp as a child a few days ago. I'm playing a 5 year old girl. I started like you did. Made an adoption panel at MAW and bought a shape and some larnia clothing. While waiting to be adopted I looked around for an orphanage or kids dorm I could rent a room in. That way I could have a home. Renting just a normal apartment felt unrealistic but I wanted somewhere to live. I just found a little kids room for rent earlier in a house with other kids just like when foster kids get put into group homes. No grown ups around though and only 50 prims but home is home. It's in a nice family community. I'm still hoping to be adopted but having fun right now
I also agree on the baby talk. It's awful. My real life son is 2.5, speech delayed due to fluid in his ears and he still speaks clearly ever since he got tubes in his ears even though he got a late start talking. No baby talk from him. I don't think rping with baby talk is too realistic.