Ok, but what created the Gate?
Good questions. To answer the first one, the "Gate" isn't really a "Gate" by traditional definition, it's more like the boundary of the Sea of Eden is physically connected in space and time to the future. Think of it like a time barrier of sorts. Once you cross it, you are instantly in the future. For simplicity's sake, we can call it a "Gate" though.
And it was created by the Time Crash, unintentionally by the Chronopolis scientists (although Belthesar planned for it to happen all along). The Chronopolis scientists were attempting to gain "power over time" using "anti-annihilation energy", whatever that means. I always interpreted as meaning that they were trying to remove Chronopolis physically from the timeline so that they could access any point in time or space they wanted. But regardless of what their intentions were, the experiment failed and instead the boundary of the Sea of Eden in 2400 AD became connected to the boundary of the Sea of Eden in 12,000 BC. And it remained that way ever since.
So in short, the Chronopolis scientists created the "gate" but they didn't mean to. It was an accident. But Belthesar knew what would happen and actually planned for it, he used Chronopolis all along and technically sacrificed the scientists for his own master plan (kind of a dick thing to do, don't you think?).
And how would Serge survive if FATE can no longer save him? I mean they travel there and see nothing, but somehow he lives?
This is the genius of TB/TTI. So in 1006 AD in the Ideal Timeline Serge and Wazuki and Miguel enter the boundary of the Sea of Eden. They are actually TB'd away at this point. It doesn't matter if they actually crossed the boundary of the Sea of Eden or not. If they waited for even a split second later they would have become Time Bastarded.
After that, Serge and Wazuki and Miguel appear in the future due to TTI. They would likely see that there is no Chronopolis or FATE, and young Serge would probably die.
But that doesn't matter, because Serge that we know and love and Wazuki would still appear at the boundary of the Sea of Eden in 1006 AD due to TTI anyways.
Remember that each instance of disappearance or reappearance in time travel events is preserved by the theories of Time Bastard and Time Travellers Immunity. So it doesn't matter that Serge dies, because another version of him would just appear in the past anyways. Confusing, no?
Or to sum it up:
Originally, Serge and Wazuki and Miguel enter the Sea of Eden (travel to the future). Then Serge comes into contact with the Flame and is healed. Then they exit the Sea of Eden (travel back to the past again). All instances of their time travel are preserved in the timeline by TTI/TB.
So in the Ideal Timeline, Serge and Wazuki and Miguel enter the Sea of Eden. They appear in the future due to TTI. Serge probably dies. But then they appear in the past due to TTI anyways. Miguel gets screwed out of living unfortunately.