Maybe a staple for those top cracks...Geo
Nope, there really isn't enough wood across that top horn for the staple repair. Staple reinforcement does work quite well with other situations.
The thinnest cracks can be permanently sealed with cyanoacrylate glue that will wick into the crack easily all the way to the end.
No, no, no... bad advice from someone who should know better by now, but doesn't. It won't add much strength, and it will act as a wood sealer, and cause blotchy spots around those filled areas when finishing. Cyanoacrylate glues (Krazy Glue) are excellent for non-porous materials, and they have great strength in tension. But they are a poor choice as wood glues. They are often used to seal grain and to help reinforce punky wood that has deteriorated from oil rot, etc. But there are better choices for that too.
The best glue I have found for gunstock repair is Titebond II. Hard to tell but that stock doesn't look badly oil soaked. But Titebond II, or any other glue, works best in clean dry wood. I've found that Titebond II gives me repair joints that are as strong or stronger than the original wood. And when the joints are closely fitted and carefully clamped, it provides the least visible glue joint after finishing. I hate a stock repair that sticks out like a sore thumb. Clear epoxy is very strong, but the glue joint line stands out more after finishing. Polyurethane glues such as Gorilla Glue are very strong, and good for filling slight gaps. But they are very messy, and stain the wood around the repair, requiring excessive sanding to remove before finishing. They are good in wood that may have some oil contamination or for naturally oily woods such as ebony.
For cracks like those around the sideplates, I try to spread them open slightly, and use a syringe to get glue deep into the crack. Draw it closed and wipe off squeeze-out with a damp cloth. Then quickly clamp the crack closed. For an irregular surface like that, surgical rubber tubing or strips of rubber inner tube wrapped around the area work great without damaging the wood.
On one sideplate stock repair on a German double, I was concerned that the clamping might pull the thin wood around the locks in too far, and make it hard or impossible to get the locks back in. So I made a dummy sideplate out of steel of similar thickness, and coated it with paste wax as a release agent, to maintain the dimensions of the lock inlet.
For cracks under the sideplates or cracks that cannot be fully closed, I use a good clear 2 part epoxy such as Brownells Accraglas or West Systems. That crack on the top of the stock heel may be tough to draw completely closed. If there will be a gap, that is where epoxy shines. Some people mix the epoxy with walnut sawdust to try to match the stock, but walnut sawdust mixed with epoxy leaves a very dark repair joint. I found that fine pine sawdust matches walnut better. You can experiment before doing the actual repair to get a good color match.
Naturally, when you pull a crack closed, there will be squeeze-out, and it is best to remove what you can before the glue hardens, to minimize staining the wood and to minimize sanding. Sometimes, I wrap the area with waxed paper before clamping with rubber tubing to keep the glue from sticking to my tubing.