I wonder who lives outside of Middle-earth and what is their life like? What are the names of the continents? Is there a big good map of Arda?
The Earth which is known as Arda in the Lord of the Rings has a few continents. The stories mainly take place on Middle Earth, but there is also The Dark Lands, and Aman which is also known as the Undying Lands.
According to the LOTR Wikia..
Not much is known about this continent, except that it formed during Morgoth's marring of the world by breaking away from the main part of Middle-earth (Endor). No Elves or Dwarves lived there, but it is possible that wild Men may have lived there at some point. The Númenóreans probably visited it on their long journeys, although it is not known if they established dwellings there. Most of the continent is covered by vast dense forests bordering much of its shorelines.
The Atlas of Middle-earth pgs. 5 & 39
The Undying Lands is actually the place that most Elves and Ainur live.
It is to the west of Middle Earth.
In the wikia it states..
The Undying Lands were a realm inhabited by Ainur and Elves. The area included the continent of Aman and the island of Tol Eressëa. The ocean Belegaer separated the Undying Lands from the western shores of Middle-earth.
The history also states that
Originally, mortals were allowed to trade with those from Valinor in the Undying Lands, but were forbidden to sail west beyond the sight of Númenor. However, in SA 3319 (Second Age), the treacherous Sauron deceived Ar-Pharazôn, the last King of Númenor, to believe that the ruler of the Undying Lands would be granted immortality and persuaded him that this was man's right and he had but to claim it. To prevent the king's invasion, Ilúvatar destroyed Númenor beneath the ocean and set the Undying Lands forever beyond the reach of mortal Men. Elves were still permitted to sail across the sea to the Undying Lands, if they chose to (which most did).
Here is a depiction of what The Undying Lands and Middle Earth look like on a map
Just to be clear the above post is not a "canon" map but a depiction of what it's supposed to look like... from the research I have done there are no canon maps depicting places other than Middle Earth... the closest thing canon wise is.. which is pre-LOTR as well...