It's NOT normal for a 2 yo to want you to read them 20 books a day
It's not?
lol! For us, it got worse for my small girl when she started walking at 12 months because she could go and get more and more and more and more books for me to read.
I had to limit read aloud time to 30 minute stretches because my voice can't take anything longer.
ETA:
I can't answer all the questions because I had no thoughts of giftedness for my big girl until she was 3 years old and 3 different teachers suggested it. Although, at her 2 year old check up, the NP estimated she was 2 to 2.5 years ahead cognitively but never mentioned anything about it.
She hasn't been tested officially but we did let a buddy administer the WPPSI-III for his Master's class.
She seems to excel verbally and in math. Her interests are math and science. Her maturity level is definitely lower. She wasn't placed into the 5-6 year old class at church because she can't sit still!
My small girl seems advanced: she object counted to 10 (missed 4) at 17 months old. Said her first word at 4 months, says all sorts of things now including sentences. She is starting to recognize shapes and colors and letters. She is also starting to work 24 piece puzzles - she can do 12 piece puzzles now.
