This was state-of-the-art in cellphones in 1989, the year Mimi turned 13 (she was born in 1976). https://en.wikipedia.org/wiki/Motorola_MicroTAC
Hella expensive, IIRC, for the phone and for the cell service. I also agree that at 13 she probably wouldn't have contact info for her siblings, especially if they were both out of the house when she got moved to California. She didn't say it, but maybe mom disconnected from her siblings and didn't have current contact info, or wouldn't share it, herself.
I could believe that she was getting by couch surfing. All it would take was a quick explanation to an understanding friend's parent(s) that she got put on the street by her mother. I grew up with kids that slept at each other's homes all the time, even during the school year (my own parents only allowed me to sleep over places or have a friend sleep over every now and then, and never during the school year). I also read somewhere that she connected with her birth father when she was 16, so maybe she got some support in her later teen years from him?