Take everything in the world. Every physical piece. Break it into the smallest slice you care to: (atoms, quarks, whatever). The count of those things is bounded. It's a huge number, but it's finite. Infinity is not a real concept, it's imaging that there is no number that can be bounded.
This demonstrate countability, not finiteness. If by "world" you mean universe, there's no guarantee that you can "take everything in it", because it might be infinite.
Not necessarily. The observable Universe could also be reducing over time. Distant galaxies are accelerating in their travel away from our observation position because space itself is expanding. This means that over long periods of time, objects at the periphery of the observable Universe will red shift out of view.
