Does a fake Rolex have a Rolex symbol carved In the glass?

Sadly, with the manufacturing technology eventually becoming affordable, counterfeiters manage to gimmick a lot of the "secret signatures" of watchmakers.

The Rolex symbol carved in the sapphire crystal can probably be counterfeited nowadays, so it makes it harder to tell a fake from a genuine Rolex.

The hardest thing to counterfeit would be the performance of the movement, so if you have a watch timer, you can easily see if the movement performs well or not. A Chinese movement will typically show a substantial variation between different positions. A genuine Rolex will perform consistently across all positions.