Hi and welcome..
First thing is to try and figure out your child and how they learn best. Then I would try to get the teacher on your side- I do this by volunteering in the classroom and helping them as much as possible. Try to keep in mind that (if they are a good teacher and care) that they want to help your child. Also understand that they often have a lot of other students too and may not know how to help your child. The good news is moderately gifted do much better in traditional schools than HG/PG. So you may just have to do some tweaking, especially if it's a good school.
As far as telling your children they are gifted, I think that it is something you have to decide - but the psychologist told my son and he says he doesn't believe it.. so.
I would try to make sure that your child stays or is grouped with other kids that are gifted. And as you figured out already, don't tell other parents your child is gifted unless they have a child who is gifted. People don't really know what it means and take it for bragging which I'm sure you've discovered. We really need a secret handshake
Also, google the following: Gifted and Perfectionism
Gifted and Overexcitabilities
