Yes it will because it gives your thumb more room.
No, the Big Ben does not have weight rings and thus there is nothing inside to fall out. Anyway, they wouldn’t fall out that easily.
The caps have a minuscule weight and thus it will not affect it much (at least you can’t tell the difference)
Yes. If you don’t destroy them by taking them out. You can just press them back in.
To take them out, I would recommend using a suction cup or a piece of duct tape and pull slightly at an angle not straight up. This will make the suction cup/ tape stay onto the cap for you to remove it.