Is there a product for filling cracks/splits?

Much depends on how wide and deep the cracks are and what your project is. There are any number of wood fillers that will take stain and paint. If the crack is wide, though, any of the fillers that I have tried will be visible after staining. Paint will cover them, though. For painted work, Milliput is excellent. It is a two-part moldable epoxy putty. It does not stain well, though. If you are limited to big box stores, both Bondo and Dap make fillers that will take stain and paint.

If you have specialty stores near you, ask for their advice.

if i can cut out the splits/cracks and re-glue, i do that. If i can't, i stabilize the board by getting glue into the split and clamping it together. you can used compressed air to blow the glue in - you have to turn the valvle almost closed so you have just a wisper of air. otherwise you blow glue everywhere.

That looks like a perfect opportunity for some butterflies or different wood as wedges for a design feature.

David

Any filler that won't eventually fall out will not likely take stain. I'd use a dark tinted epoxy to fill them in.
But the chances of them just cracking somewhere else will still be very high, as it's nearly impossible to dry slices like that without them splitting apart.

As you close up one crack, another will appear somewhere else. Although there are fillers that take stain and finish, they are not likely to look very good.

Forget everything that I advised in my first post. I didn't understand that you were dealing with slices with the pith in them. Any of those that have not spit yet will. It's the nature of wood. Anything that you put into those cracks will fall out when the crack opens more.

Thanks for all your suggestions. To the woodpile with the split pieces.