I haven't used Box2D myself but it's popular and I've heard it's pretty easy to work with.
Yes. Box2D is a physics engine, not to be confused with a full game engine. Box2D will handle your physics but you'll need to render elsewhere using OpenGL, LibGDX (taken from your other thread), D3D, or whatever. You would probably have the rendering done in one class with the physics handled by another. A Physics Engine will only handle physics. A Game Engine, on the other hand, will handle a multitude of things, including physics, rendering, networking, and such.