Purchased content for minecraft won't complete downloads

We have tried that. It still won't recognize that we have downloaded the content. As soon as it says download complete, he goes into the game and it shows everything is purchased but not downloaded. Or shows that there is new downloadable content available.
I'm beginning to wonder if it is something wrong with the xbox itself

When you purchase content it's tied to the gamertag that purchased it as well as the console it was purchased on. As long as you're using the console with the gamertag that downloaded the content, then you have access to the content. It's set up to work
that way and won't result in a ban.

If you switch consoles, you won't have access to that content anymore.

It's a known issue that if you purchase content through the sales and specials app it won't show in the marketplace as being purchased. But you should be able to redownload the content from your download history -

support.xbox.com/.../download-content-history

The original game was removed that's why you don't see it on the marketplace

This does not affect your download history though you can download any content from the download history

It was replaced with the Xbox 360 version last year

Which won't show as purchased since its a completely different package

I'm assuming they use prepaid points cards for the region they are registered to. Even then, there's no guarantee that purchasing the content on the account will allow you to download it completely. There is some content on Xbox LIVE that is region locked.
There's no way to know what is or isn't. If you purchase something that is region locked, you will not be able to complete the download but you might be able to complete the purchase.