Is it true that the Prophet (ﷺ) is alive in his grave and if so what kind of life is that?

The Prophet (ﷺ) informed us that the earth does not eat the bodies of any of the Prophets not just himself. From that people have concluded that the Prophet (ﷺ) is alive, however the Prophet (ﷺ) is dead, as Allah (سبحانه و تعالى) says:

“Everyone shall taste death…” [1]

From this verse we understand that the Prophet (ﷺ) is dead. Whenever we ask Allah's peace and blessings upon him, Allah conveys them to the Prophet (ﷺ) through the Angels and equivalent blessings from Allah and the Angels will be given to those who do so but this has nothing to do with life as we know it. That is why the Prophet (ﷺ) said:

"...Pray for me wherever you may be."[2]

Some people think that he (ﷺ) is alive in his grave so they can go to his grave in Madinah and give greetings to him in the mosque where he is buried, and ask for Allah's blessings upon him and so on. It is not a requirement; it can be done anywhere because it is carried to him.

References:

[1] [Quran 3:185]

[2] [Sunan Abi Dawud 2042, Saheeh Al-Albani]