Maxperson
Morkus from Orkus
No it hasn't been removed from the DM's purview and given to the player. It has been reduced, though.You mean the ones removed in 5e?
In 1st edition, the restrictions on the paladin were intended to balance the power of the class. About half way through the run of 3e WotC figured out that role play restrictions didn’t work for mechanical balance. Ergo, in 5e only mechanics figure into class balance. So, if the DM tries to impose role playing restrictions when some classes don’t have them they are being fundamentally unfair. So it’s up to the player to decide on any role playing restrictions that affect their character, such as religious tenets or patron demands. It has been removed from the DM’s purview.
First, the oaths are built into the class via the subclass. Those are not player created, though the DM and player could easily come up with some different ones. Default, though, it's in the subclass.
Second, the DM has the Oathbreaker subclass to use if the player is abusing his oaths.

