Immortality means you never will die from natural causes (old age basically), the word I think people are thinking of is 'invincibility' which means you cannot be killed.
An immortal creature will live forever unless its killed (or dies from an accident or runs out of food or whatever), it will never die of old age. An invincible creature is impervious to all attack and cannot die (unless hit by a projectile fluffy wambler).
As for magma.. I never touch the stuff for fuel anymore. To me its one more 'easy mode' thing these days (by which I mean its available on every map, its easy to find, its easy to use, and gives you unlimited fuel). Using magma for traps is something I don't personally bother with either but at least weaponizing it requires some skill and ingenuity, that I can respect.
As for the OP; digging down (as has been stated) gives you access (often) to more metal, gems, the caverns (which have interesting monsters and other features in them), flux stone, magma, and ultimately..
(spoilers)
Rare and powerful metal and access to 'hell', which comes complete with demons so be careful.
Whether these things are things you want or not is up to you. Depending on your mods or gameplay settings the surface world can be as much or more dangerous than anything you'll find below (short of the bit spoilerspaced above), for example using mods such as Fortress Defense will add literally hundreds of enemies to come after you.
As for dangers.. That is sort of what this game is about (unless you are using it to make megaprojects). Coming up with more challenges is the way a lot of people play, and eventually the tried and true standard of "Build walls and fortifications and drawbridges and have crossbow dwarves pepper the enemies with bolts until they die or leave" gets dull (to many of us).