Can I backup Xbox 360 games to the Xbox One console, and play them without the disc, like...

You can play any backward compatible 360 game on an Xbox One, provided you can either install it via disc like on the 360 (and the disc will need to be in the console in order to play the game), or you have purchased the 360 game digitally so you can download
it to the console.

If you purchased the all digital Xbox One S, you will need to purchase any 360 games digitally (even if you already own them on disc) in order to play them on that particular console.

unless you own the digital version of thwe game then the disc must be in the drive to authenticate ownership, so with the series s you will be unable to play xbox 360 games from disc.

Hi,

The Xbox One can't read and run the data directly from BC 360 game discs. The games don't run from the discs like they would on a 360 console.

When Microsoft made these games BC, it took the original games, and without getting into all the technical details, reverse engineered and repackaged them as a digital downloads so that the Xbox One can play them. This is why as Smwutches as already stated,
there is an 'Update' when you insert a BC disc 360 game into your console. This isn't an update, it's actually the digital version of the game.

This is why your 360 game 'updates' are around the 8-16 GB sizes. Still comparatively small compared to the average Xbox One digital game download.

The BC system for 360 games on the Series X will have to work the same as there is no other way to do it.

However, the Series X is architecturally similar to the Xbox One, so Xbox One games will install and play on Series X just as they do an on an Xbox One console.

What about disc games because I only have a couple digital games the rest are on disc and samething for the Xbox 360 Games also

All saves no matter what type digital/disc or even 360 are all cloud. Just make sure you are connected to the internet so it can back them up. You can force a backup in settings.

Also this may help: https://support.xbox.com/en-US/xbox-one/console/back-up-your-settings

You most likely won't get $100 for the Xbox 360 when the next-gen comes out. But, aside from that, remember the crippling red ring of death after the Xbox 360 launch? It would be best, if you can't live without your console (like me), to keep the Xbox 360
for a while as backup were anything to go wrong after you adopt your new next-gen baby. I, personally, have never had the RROD problem. But, I can imagine how distraught I would have been without a backup console to game on.