What does that symbol warning and the Disc mean ?

Hi Steezzy. My name is Kyle and I'm an independent advisor.

The symbol means that the disc for this game isn't inserted in your console. If you insert the game disc the symbol will disappear and the game will be playable.

Thanks,
Kyle

Hi there,

I think it's just an icon that they added themselves in their profile name, in such case it doesn't mean anything at all.

Same for people using a 'verification' check-mark, doesn't mean a thing either, it's not something official.

Side not, the other symbol isn't the Ambassador symbol, it's just the Xbox Logo.

There is also one that has multiple little avatars that means that you are able to join the game.

Controller - Playing a Game/At the Dashboard

Circular Arrow - In a joinable session.

It's a badge to commemorate the ending of Gold.