how can a fissure split a continent and an ocean?

Answer 1

The type of fissures you're talking about are at crust level.
Considering that the oceans are on top of the earth's crust (they're basicly huge lakes) it's perfectly possible for a crack in the crust to run thru a continent and an ocean.

You should consider that the crust is a huge tract of land and the continents are like mountains on that land. Since they are 'tall', they rise above the sea.

Answer 2

The continents are sitting on top of pieces of crust that are moving around on top of the mantle - the next layer down. The process is probably powered by convection currents in the mantle. The plates are moving at about the speed that a fingernail grows.

The movement of plates is largely the cause of earthquakes, most volcanoes (Hawaii and Yellowstone are in the middle of plates but are powered by hotspots) and the raising of mountain ranges. Where the plates are pushed together one dives under the other which pushes one up to form mountain ranges, like the Himalayas, the Andes and the southern Alps of New Zealand.

In other places the movement tears land apart. The African Rift Valley is one such place, but most separating is done along ridges in the middle of oceans.

All the activity is called plate tectonics.