If one continent sank into the ocean what would happen to the rest of the world?

The ocean is on tectonic plates which continents are also on...this question shows a fundamental lack of understanding of plate tectonic theory since its very nature is improbable.

It's obvious that most part of the earth is covered with water and any increase in the level of water without a balanced cycle may likely cause a flood. notwithstanding the fact that level of water fluctuate from time to time and from region to region, definitely if a whole continent will submerge the other parts of the world will be heavily flooded completely, especially the southern hemisphere where there will be an undefinable and incalculable planet degradation.

if a continent sank down into the ocean, the ocean will displace the volume of the continent which can cause small islands to disappear and half of the other contienents to be covered by water

Felsic continental crust cannot sink into the mantle. It is less dense by an average of 600 kg per cubic meter and therefore very buoyant. Sea level change by melting ice, isostatic rebound or tectonic uplift can only modify the coastline by so much, or move stuff around. In no case will a continent simply sink

That continent couldn't sink into the ocean. The only thing that would happen along those lines would be a continental plate sinking submerging and an oceanic plate, and that doesn't mean sinking into the ocean.

My guess is the water would rise due to such a huge mass underwater

One less nation to threaten us.