Is there scientific proof the sound of a French horn will change when the bell is made detachable or has been lacquered?
There's no evidence that cutting the bell makes any perceivable difference in the tone quality. If it did, professionals would go for one piece bells despite the (slight) inconvenience of a more awkwardly shaped instrument case.
I'm not aware of any scientific studies, but many people claim a noticeable difference between a lacquered horn and an unlacquered one. I've never had the opportunity to A/B test two otherwise identical instruments, but from my experience I'm inclined to believe that there is some slight difference. However, there are other reasons to prefer one or the other that have nothing to do with sound, so just because someone has chosen one particular finish doesn't mean they've done it for tone reasons. For example, I need raw brass because my acidic sweat will burn through lacquer and silver plate.