One or two times probably not but more than that likely will. Especially if there were major dents you grinded away. You can buy a cheap plastic tool to check the balance and then just grind away from the non blade side to balance it out.

It can, yes. Remember these are rather heavy blades spinning really fast, so it doesn't take much.

It really depends on your definition of balanced and how bad someone is at sharpening.

The blades are torqued down on there, if it's a combustion engine mower, nothing's you do to this blade sans taking an inch off is going to make much more vibration than the motor will itself.

The biggest worry is that you put enough vibration into it too cause it to loosen the blade.

If you're even half reasonable sharpening you're just taking off a fraction of a gram.