Q: How is the bolt operated?
A: The K31 is a straight-pull bolt action rifle. This means that you pull straight back on the bolt handle (some are "red" (ish), some are made of metal). The bolt itself is designed to rotate in spite of the bolt-handle traveling back and forth in a horizontal path.
Q: Do you pull the ring or pull back on the red handle, or both?
A: To operate the bolt, you just pull back and push forward the handle. The ring is part of the striker, it is a cocking indicator and it controls the safety. To put the rifle on "safe," you pull back on the ring, twist it until it is horizontal, and you release it. It is one of the most reliable mechanical safeties of which I know.
Q: Do you push closed with the ring or handle?
A: With the handle, as I have said above.
Q: Can bolt be operated by a lefty with the right hand without cutting the left hand kept on the grip?
A: Only if you keep your thumb to the left of the stock (as some shooters do). If your thumb goes over the stock, the bolt will come into contact with it.
Note: the 1911 and the K31 do *absolutely* shoot the same ammunition. The mechanical difference between the two is that the 1911 action has a longer bolt-travel. You can easily tell the two rifles apart because 1) the 1911 is a full-length rifle, 2) the magazine is located farther away from the trigger-guard (hence the longer action).
It is the Schmidt-Rubin 1889 that only takes the lower-pressure cartridge and should never be fired with regular post-1900 Swiss ordinance ammo.