How was Gabriel (peace be upon him) able to move between heaven and earth to deliver the message to the Prophet Muhammad (peace be upon him), and was there a special opening for him and for the Prophet (peace be upon him) during his ascension (Mi'raj)?

Allah Almighty created the Throne before the Pen, and water before the Throne. There is no explicit evidence that the earth was created upon water. The order of creation is water, then the Throne, then the Pen, then the heavens and the earth.

Gabriel, peace be upon him, travels between heaven and earth by the power of Allah Almighty. There is no specific opening for angels to ascend to heaven. The Prophet's ascension, peace and blessings be upon him, to heaven was by means of a device called "Al-Mi'raj," which resembles a ladder. There is no benefit in delving into details for which no sound evidence has been established.