Definitely not. The "Dress" phenomenon proved that there are certainly things people perceive drastically differently from others, that unless explicitly pointed out would rarely be noticed.

Perception of reality is not the same for everybody, but there is a single objective reality that we all perceive in our imperfect ways.

That is just speculation. Maybe the only things that exist are subjective perceptions and they don't all overlap. Then the objective reality only exists from god's viewpoint, so if there's no god...

If there is no objective reality, then what is the explanation for the overlap of our subjective experiences? By the way, you do bring up a good reason for the existence of God as the only one who knows all of reality. However, God does not know reality by perception. Rather, God is the source of reality, so he knows it because it begins in his mind.

Is this "subjective perception" part of the "objective reality" or somehow outside of it?

Subjective perception is part of objective reality. Or rather, it arises inside objective reality.

Not that I could conclusively proof that statement.

The answer is NO.

We all have our personal realities that operate on their own timeline. Only when you are playing an MMO next to someone do you get a chance to notice it. But it exists both in game and in real life.

In as much as information to our knowledge propagates no faster than speed of light in a vacuum, in one sense reality can not be the same for anyone.