There are plenty of new game releases on used disks sold online(for example on amazon) and the price of the disk is almost always lower then the new one. Are there any restrictions or account bindings when you buy a used game like that? Or I can just buy the disk, install it on Xbox's hard drive, bind to my live account and play without any fear?
You will have no problems using the disc.
When the Xbox One was first announced, Microsoft introduced a model where newly purchased retail games would be licensed similarly to downloadable titles; you wouldn't need the disc to play if installed, and you'd be able to download and play the game with your Live account on any Xbox One console. However, this restricted used games, in that if you wanted to sell a retail game you'd have to go through a special deauthorization process that would only be offered at certain retailers (like GameStop) and would only be available with the game's publisher's consent.
Backlash to that model led to Microsoft adopting the same model as every other console, past and present: if you have the physical game media, you can play the game. In the Xbox One's case, you can still install retail games to your hard drive, but you'll need the disc in the tray to play.