Excellent questions! When all the continents were last joined together, the supercontinent they formed was called Pangea. Pangea, in turn, broke into a northern Laurasia and southern Gondwana. Later, these landmasses subdivided even further.

The continents are embedded within plates--most plates are composed of both continental and ocean crustal components. As continents rift apart from one another, the "gap" between them is filled with new oceanic crust (a process that occurs at mid-ocean ridges). Since Earth is staying the same size, that means that at other places on Earth's surface plates are swallowed up, that is, pushed deep into Earth's interior. The places this swallowing of plates takes place are called subduction zones. Subduction zones consume only oceanic crust, not continental crust, because the former is denser, and it becomes even denser as it ages. As it gets denser, it sinks, ultimately subducting.

This process is more easily understood with animations than with words. Fortunately, there are plenty of great animations. Here's one, and here's a source for a whole bunch more.

Happy exploring! I hope this information convinces you that plate tectonics is occurring, leading you to stop qualifying Gondwana as "supposed." Just as we can confidently say that "the moon is going to rise tonight," we can say that the continents are moving--there's no doubt about either of those statements.

Gondwana was a continent created by the breakup of the supercontinent of Rodinia during the Riphean through Ediacaran periods, between 800 and 600 million years ago. It remained a separate continent until the formation of the next supercontinent, Pangaea, during the late Permian period, culminating up to 250 million years ago. Pangaea then broke into two continents, Laurasia and Gondwanaland, close to 200 million years ago, and Gondwanaland continued to break up with the last chunks (Australia and Antarctica) becoming separate during the Eocene, about 50 million years ago.

As the names might indicate, Gondwana and Gondwanaland included most of the same pieces of landmass, but there are a few differences due to the differences in the locations in the rifts that broke up Pangaea versus the collision zones that created Pangaea. For example, before Pangaea formed, the landmass that would become Florida was part of Gondwana, but when Pangaea broke apart, Florida went with Laurasia (and then later, when Laurasia broke apart, into North America). Apart from Florida, the modern landmasses that made up Gondwanaland (and thus Gondwana before it) include South America, Africa, Arabia, Madagascar, India, Australia, New Zealand, and Antarctica. There is some debate as to whether New Caledonia was part of Gondwanaland, or whether it was ever part of a continent.

The other continents that shared the world with Gondwana include Laurentia (now most of North America minus the east and west coasts), Avalonia (Newfoundland, Labrador, most of the UK, and part of France), Baltica (the rest of Europe and eastern North America excluding Florida, again), Siberia (most of the former Soviet Union), and Sinia (China, Vietnam, Malaysia, Indonesia, Thailand, Burma, etc.). There were also several terranes that could have been miniature continents around the southern coasts of Baltica and Siberia, including what are now Iraq/Iran and Tibet.

Volcanic arcs such as Kamchatka, Japan, the Philippines, and Cascadia (the last of which has become joined to western North America and is now most of California, Nevada, Oregon, and Washington) were not part of continents in the time that Gondwana was a continent.

I'm not sure I understand the rest of what you are asking (especially the crust 'pushing against itself'). Ocean crust gets subducted underneath continents when continents slide over them. Continents don't subduct, which is why the pieces of all of these ancient continents are still on the surface of the Earth.

There have been many supercontinents throughout Earth's history, which is made possible by recycling oceanic crust.

When two tectonic plates push against each other (which is essentially always happening on at least one side of a plate, since there isn't any space in between them), one of two things can happen. If at least one of the plate boundaries is oceanic crust, the denser oceanic crust will be subducted down into the flowing part of the mantle, and its material is recycled. This is what is happening on the West coast, where the Pacific plate is being subducted under the North American plate. Continental crust is much lighter than oceanic crust and typically cannot be subducted. If there is continental crust at the edge of both plates (because all of the oceanic crust between the continents has already been subducted), then the crust piles up and forms mountains. This is what is happening in the Himalayas, as India (formerly a separate continent) pushes into Asia. Since a plate can only move in one direction at once, the side opposite the collision must be pulling away from another plate. New oceanic crust rises between the two plates to form mid-ocean ridges, so the total amount of crust is preserved. Oceanic crust does not get more than 150 million years old before it is recycled, so geologically speaking, there is plenty of time for it to "get out of the way" as supercontinents form. Continental crust, on the other hand, can last for billions of years, since it isn't subducted. This is why there are still recognizable continents after supercontinents come together and break up again.