I tried to not accelerate - and so did the school. Social problems got worse and worse until he was getting beat up on the playground weekly (in 1st grade). Came home with headaches and vomiting **every day** after school. He would cry and beg to "stay home and do workbooks". He went from the popular kid in preschool and 4K to a social outcast by 1st grade.
In 1st grade, he was doing 4th grade work (as tested by the school) and neuropsychologist said he may or may not regress to the mean over time, but it was unlikely given how far ahead he was then.
I enrolled him in a public virtual charter school where continuous progress acceleration is their norm. That's when things got crazy with acceleration. In math, my son skipped 2nd, 3rd, most of 4th, did 5th grade in 2 months, refused to do 6th grade and skipped to Algebra 1. In english, he skipped 2nd, 3rd, 5th, 7th, and 8th. He did not regress to the mean! LOL
I found radical acceleration to be inevitable and necessary. Observe your child. When the cons of staying with agemates outweighs the pros, it's time.
If you prefer to avoid or delay acceleration, I think the most effective action a parent can do is to resist the desire to "afterschool" supplement a bored child with academics. Rather, supplement with non-academic but intellectual activities, like music lessons, animal training, computer programming, etc.
The answers to the rest of your questions are best answered by the book "A Nation Deceived" which is available free online in PDF format.
