Is the time-lock on Gallifrey gone, so Clara was able to land, or is there more going on? Did the Doctor ever realize Clara had managed to land on Gallifrey?
Firstly, I think you're confusing the "time lock" on the result of the Time War, "The Moment", which was the weapon The Doctor used, and his later plan to save Gallifrey by putting it in stasis. They are all very different things.
The device known as "The Moment" (also known as "The Eye of Discord") which, in his incarnation as The War Doctor, he used to end the war, was a weapon "capable of destroying Gallifrey, the Daleks, and whole galaxies within a single moment". Its name comes from how quickly it can destroy, and has nothing to do with freezing things in a moment of time. The Time Lords harnessed the power of black holes with "The Eye of Harmony", so you can imagine that this weapon would have at least the magnified destructive power of a black hole.
So The Doctor did actually destroy Gallifrey and The Daleks, putting an end to the Time War. The events of the Time war are "time locked", meaning that time-travel to them was not possible. Nobody should have been able to travel into the war, and nobody should have been able to break out of the time lock. However, as we know, both Daleks and Timelords did find ways to break out of it - Dalek Caan got out, but at the cost of his sanity; Rassilon and the Timelords used the beat inside The Master's head as a signal to fix on outside of the timelock and attempted to break out from it that way.
It was the AI of The Moment (taking the form of Rose) that broke the Timelock allowing the three Doctors to return to the Time War:
TEN: These events should be time-locked. We shouldn't even be here.
ELEVEN: So something let us through.
MOMENT: You clever boys.
Once there, the new plan to save Gallifrey was based on the technology of statis cubes - to freeze Gallifrey in a moment of time.
The Timelords explained what the result of this plan would be:
"We'd be lost in another universe, frozen in a single moment".
So, the war would remain time-locked, but Gallifrey would survive elsewhere in the universe. The planet was "lost", and The Doctor said he was going to look for it - but it found him first. The crack from Amy's wall, which we learned was a crack in space and time, apparently linked Gallifrey to The Doctor as Clara was able to speak to them through it. From the point at which Gallifrey was "saved", it was not impossible for The Doctor or The TARDIS to go to Gallifrey - just very, very difficult.
Onto the question of how Clara managed to "accidentally" land the TARDIS on Gallifrey - The Doctor had connected her with the TARDIS telepathic interface and it "extrapolated" her entire timeline. He was trying to locate the moment in time that she first had the dream about something under the bed, but what he did not reckon on properly was that, as "the impossible girl", her timeline is connected with all his own timeline, and evidently, this allowed the TARDIS to travel to the moment that The Doctor had the dream as a child on Gallifrey - which turned out to be, paradoxically, Clara under his bed.