Should gold tips be on the top and bottom copper layers for PCIe golden finger?
Gold tips should be on the top and bottom copper layers, right?

Correct. Gold doesn't oxidize, so always presents a clean metallic surface for good electrical connection. The pins are also commonly accessible by end-users, whom like to touch them.

Should I do hard gold plating?

This depends on the application.

If a prototype board and you're anticipating limited insertions, standard tin plating is fine. The tin will wear away slightly with each cycle, eventually failing and possibly contaminating the connector. But you'll have spares, and anticipate this and be able to fix it easily.
If a final board and anticipating limited insertions, ENIG gold may be fine, such as OSH Park. The gold makes good electrical contact, but is slightly worn away each time. The gold layer is really thin, and ideally would only be inserted once.
If a final board and anticipating repeated insertions, &quot;hard gold&quot; plating is chosen. This is a thicker layer of gold and better process for depositing it. It still wears away, but since it's thicker, it will tolerate more insertions before failing.


Is it necessary to have beveling?

This depends on the connector and application. Some connectors are designed to accept an un-beveled edge, while others may refuse to mate with it. I would suggest getting one of the connectors and trying the fit. You may find that sliding a fine diamond-file (at 45 degrees) once across both edges is enough to allow the connection to be made.

For prototyping use, it is understood that connectors might be a little more finicky than for a final design. The intended audience is also well-versed in electronics.
For a final design, the intended audience is the average consumer, with possibly zero understanding of connector mating principles and experience. So the easier and more reliably that connection is made (bevel), the better.