Help! My toddler is weird. Is this normal?

I'd like to start with the fact that she's my first born and only child, so I have no idea how other children behave.I'm concerned about a series of weird things she does:At 2 months she would repeat after me all the vocalsAt 6 months she started having an imaginary friend who she would talk and play withShe plays only with kids around the age of 8 years or older and runs away from kids her age (2).At around 1 3/4 started to sing the ABC (I never tried to teach her the alphabet before that)She sings songs she hears on the radio/tv even after days from when she heard itShe closes herself into a bubble and seems like she cannot hear youShe remembers where things at the store are (example where the bread, bikes, cooking tools...)She puts in order the notebooks and clothes at Wal-Mart and makes a fuss if you stop her.She thought herself how to eat with the fork and even rolls the noodlesShe tells jokes and talks back like a teenagerShe's obsessed with numbers and she counts things randomlyShe's obsessed with puzzleShe pretends to be a doctor and gives random suggestions after the "surgery" on what to do or not.She hunts monsters with the flashlightDoesn't want me to help her with anything (getting dressed, going potty, getting food...)Opens books and pretends to read while telling you a story based on the picturesShe asks too many questionsShe does not nap (she generally sleep from 22 to 8)My thought is that she might be a special need child (autistic) or maybe with some kind of mental illness (runs the family). What's the next step? Her pediatrician doesn't believe me or says she never heard of something like that (in her defense she's kinda slow, she once asked me if we have toilets in Europe).TL;DR: Two year old toddler is weird, I think she might be autistic or something. Help. via /r/Parenting http://ift.tt/2elRdK5