Speaking of Paladins can they still lose powers by morally impossible situations in 5e?
Paladins have been reinvented more than any other archetype in 5th. First, if they are put in a morally impossible situation or simply screw up a little, there's no power loss. Instead, the paladin will usually do something in line with their own tenants to atone(a night in contemplation, fasting, etc.). Their oaths are more what they aspire to now than what they are.
This also means that alignment has gone out the window. All Paladins stand against evil, but there's now room for evil paladins that haven't fallen. There are three oaths outlined in the PHB(Oath of Devotion, Oath of the Ancients, Oath of Vengeance), which are supposed to roughly align with LG, NG, and CG, respectively. Taking one of these oaths means that your character has some good aspects, and being a paladin means that they are devoted to stand against evil of some kind, but neither of these things force you into a good, or even non-evil alignment. Of course, the path of a paladin is overwhelmingly more attractive to good, but they've intentionally left a lot open to the player now.
All of that being said, forsaking your oath entirely will lead to the loss of your Paladinhood. It looks like fallen Paladins(called Oathbreakers now) are going to be outlined in the DMG.