Was the RAI for the best quality of the Turbo-weapon battery upgrade intended to give both +1 range and +5 BS or just +5 BS?

Difficult to tell. Most components also explicitly say that Best quality also grants Good quality upgrades, while the Turbo-Weapon Batteries don't have that.

Hard to say what was intended by that ruling, but I think you could probably make an arguement that it should grant both. I wouldn't though, as honestly I would swap around +5BS and +1 Range for Good/Best.

Thank you for responce Erathia. You suggestion seems reasonable as +1 range is a better bonus then +5 BS.

Well.. Common sense and precedence state both. But +1 Range is inherently way better than +5 BS, in most cases.