Support, and love are important, but so is understanding. I would advise that you refer to them as male, as your son, use the name he wishes you to.
Even if you have your doubts, these measures will help them to explore who they really are, and they will feel safe doing so. If you insist on calling them she, female, daughter, etc, then you are not being supportive, and you could get pushback.
If they decide that they are not male? No worries, you gave them they chance to explore, and made sure they were safe to do so.
If they decide that they are male? No worries, keep supporting them, they are your child!
I can't offer any advice on binding, but I would encourage that you set some rules on this, so for example, not around the house, the house is a safe enviroment, and should be judgement free. This means the chest isn't getting squeezed all the time!
Sports bras may also be the way to go, I know one poster said they are just as bad, but not really, depends what you get. I have to have them for disabilities, here's one from Decathlon that I have - www.decathlon.com/collections/womens-sport-bras/products/running-zip-sports-bra-117165?
It's got amazing padding, it flattens the chest, and it doesn't exactly look feminine! I can also tell you, my cat loves sleeping on it.
Hope this helps!