If you are not a Mexican citizen, yes you do.
yes. you MUST.
You need to fly there. There are no boats that go to Cuba. If you are a US citizen you need to fly over the Bahamas, Mexico or Canada to get in.
can a mexican without a passport fly to mexico with just a birth certificate?
You only need a passport; nevertheless, most airlines will not ask you for such document.
You can fly to Mexico, but, you won't be able to fly back to the US.
Yes, even if you fly directly from Canada into Mexico you need a passport.
If entering Mexico trough land, no you don't need it and only an ID or birth certificate will do. On the other hand, if you fly into Mexico, you must have a passport.
Yes, you need a passport to go from the U.S. to Mexico because Mexico is not part of the U.S. If you were going to a U.S. territory and you were a U.S. citizen, you would not need a passport.
If coming from the US, Canada, Europe or Japan, all you need is you passport. Otherwise, you will also need a visa issued by the Mexican government.
Of course you can. Mexico does not have movement restrictions of any kind.
Within? Yes. From outside? You also need a visa, issued by the US government on the US Embassy in Mexico.