Foremost, this is more a matter of visual ability on each eye isn't it? I'm right handed but fire shouldered weapons left handed due to seeing better with my left eye. Took just a few hours to get comfortable with it.
I have no definitive answer for you, but I think there is none. I can only see three realistic possibilities and reality is probably all three:
1. Left handed operating the rifles the same way right handed did.
2. If not, then (goes for everyone) either use the left arm to awkwardly operate the bolt (a must if having to stand or rapid fire), or
3. Keep left hand in place to hold rifle, operate bolt with right (rifle barrel will of course dip each time, but should be no problem when having something to support the weapon on).
Being right handed but operating it in the left hand when reloading seems like a tricky feat. Using the weak hand to guide the stripper clip correctly, then push in the 5 rounds.
Modern rifles can be configured for left handed shooters. Maybe rifles back then could as well?
Unlikely. Spare parts and repairs would cause logistical problems. Not something good when supplying tens of millions of serial produced weapons. Would be better to let them shoot right handed, or even awkwardly with the left. If having too many vision problems, then assign them to some other duty than front line infantryman. Like being a horse technician.