Black walnut husks make a great dark brown stain...you will want to wear gloves

No matter what you stain it with any cut marks will cut through it and show the lighter wood under it. I would give it two months of daily mineral oil soakings and enjoy it for what it is. You'll want to maintain the mineral oil once a month after the daily applications so it doesn't dry out again. You'll also see the cracks get much better as the wood gets healthy. Use of bees wax to fill it will not work. The wood will absorb all oils out of the wax causing the wax to shrink and just look nasty.

Can you not just sand it down and oil it with olive oil (on the top food surface at least)? My cutting boards and various wooden bits and bobs look just fine as such, and I never have to think about whether its food-safe or not.

You can use olive oil but it does rot over time. Mineral oil is better as it is designed to be ingested so it's 100% food safe and will not go bad.

Ahh, I see what J. Aaron does for a living so I'd suggest you listen to him! My olive-oil bits are of course much smaller than a free-standing block so they get washed frequently and there isn't (I don't think!) much if any chance of rot. Good point though!

You can buy food grade oil to treat your block. It was purchased at local grocery store so easy to get. I did one and was amazed at how dark it got after 3 coats.