Scenario is this:
Player A has Future Sight, and a Doom Blade on top of Library. In Player A's deck there is both Oblivion Ring and Ultimate Price to be found. Player B has Dragonlord Atarka and a Stormbreath Dragon.

The original question is:
Can Player A start playing Doom Blade, as described by 601.2, and see what lies beneath Doom Blade before choosing targets?
Note: Doom Blade moves from top of library in 601.2a, and targets are chosen in 601.2c

The answer is No. Due to rule 401.6:

401.6. Some effects tell a player to play with the top card of his or her library revealed, or say that a player may look at the top card of his or her library. If the top card of the player’s library changes while a spell is being cast, the new top card won’t be revealed and can’t be looked at until the spell becomes cast (see rule 601.2h). The same is true with relation to an ability being activated.


So far so good. But! What if player A has a Sphinx of Jwar Isle? Does the Magic Golden Rule step in, allowing Sphinx to overrule 401.6?

My guess is that it is like playing Explore Like an instant; You are still not allowed to play a land during your opponents turn. But when which rule has precedence is not all that clear.

No, you can't look at the card during the casting of Doom Blade, Sphinx or no Sphinx. This isn't a case for the Golden Rule, because the rule you quoted actually explicitly covers Sphinx of Jwar Isle's effect:

401.6. Some effects tell a player to play with the top card of his or her library revealed, or say that a player may look at the top card of his or her library. If the top card of the player’s library changes while a spell is being cast, the new top card won’t be revealed and can’t be looked at until the spell becomes cast (see rule 601.2h). The same is true with relation to an ability being activated.