Can I conquer the world?

As of the current version of Dwarf Fortress, nothing happens in the world post-world gen.

This means (among other things), that civilizations cannot go extinct, animals won't repopulate, and towns will not change "ownership".

While Toady One (DF's developer) has expressed an interest in the ability to send your dwarven military out to assist in wars, battles, etc, nothing of the sort is currently achievable in-game.

So, sure, you can kill everything wherever you embark... but they won't acknowledge the fact that you've conquered them.

If you're more interested in a world without elves and necromancers, your better bet would be to tweak the world-gen parameters instead.

While you can't do so in Fortress Mode, it's (technically) possible in adventure mode to kill everything.

ERRYTHANG