Lots of good recommendations to make the toe repair, take your pick and then take your time! Theres no hurry, the rifles already over 100 years. Ive seen some really tidy repairs to stocks, that have retained the character, patina, and stock finish of the original.
Looking at your pics, the butt plate looks like it is a bakelite type material with similar characteristics to old plastic. Another alternative to what has already been suggested, would be to go to a golf shop that does club repairs, and ask for some of the epoxy that they use to repair the faces of "woods". Its hard as the hobs of hell, sticks like the proverbial, and easy to work with. Leave the butt pad on the rifle, but take the old broken piece. Use a heavy tape to form a mould on the stock, stand it on end and pour in the epoxy. When its good and dry, finish it off with a small file or sandpaper glued to a small piece of time.
Ive had 2 butt pads fixed like this, and they have stood up to a few good years of serious hunting, the join is invisible.