In addiiton, the chicken loses some flavor when frozen/defrosted, so expect the same from freezing after cooking. You may have to re-season. I cool foods I'm going to freeze completely in the fridge, and then wrap for freezing, otherwise the condensation turns into ice crystals on your food and can ruin the texture, as ChezSuzanne said.

Definitely. But make sure the chicken has completely cooled before putting in the freezer. Otherwise the condensation from the heat will freeze, which will affect the texture when you thaw it.

Yes, you can freeze the cooked end product.