Where everything leads?

To chaos.
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Eventually everything leads to chaos. This is called the chaos theory. Because of a principle of thermodynamics: the amount of entropy will increase inevitably. This means that disorder will always increase and never decrease. This leads to chaos at the end. Entropy is disorder, in every level: in macrocosmos, in microcosmos, in our daily lives. If you drop a coffee cup and it brakes to floor, it will be broken, it cannot be fixed back intact. The time runs only forward, it can never, in any circumstances, stop, or run backwards. The broken coffee cup don't collect it's pieces together and jump to the table again. It's entropy has increased because it broked. Eventually all things broke, die, and cease to exist. Entropy of everything will increase by time. The longer time runs, the more entropy will increase. Eventually leading to chaos. If you build a house, someday it will fall apart. Someday you will die, your body falls apart. Someday in far future the whole Earth will be destroyed by the Sun's last breath and eventually the whole Universe will fall apart to chaos.
But, as predicted, probably a new Universe can be born out of that chaos. All the matter of the Universe thickens into a new Singularity and a new Big Bang starting everything all over again.

Is the World going to end?

Yes. Eventually.
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But not in a long, long time. Nothing is permanent in the Universe. Nothing lasts forever. The Universe was born 13.75 billion years ago (433.6 x 10¹⁵ = 13 750 000 000) and it will live very long, yet unclear amount of time forward. The Solar System and the Earth were born 4.54 billion years ago (4.54 × 10⁹ = 4 540 000 000). The Sun gives light and warmth which are necessities of maintaining life on Earth. Sun is a star and stars use nuclear reaction (fission and fusion) in their cores to change elements to another. Sun uses hydrogen and transforms it to helium which creates massive amounts of energy. That gives the light and warmth of a star. When all the hydrogen is transformed into helium, Sun will enlarge to Red Giant, which is much bigger star than its now, and red in colour. Red Giant is so much larger than Sun now, accordingly much closer to Earth, so it will make living on Earth impossible. It comes so hot in here that everything will burn. If Sun doesn't devour Earth itself, it will burn it to dry rock. When Sun has thus used all its left powers, and blow its utmost gas spheres out to the space, it will shrink to a White Dwarf, which is relatively cold core of a star which lights just a little white light and doesn't really produce much warmth. The Solar System will get even colder place then and life in it would be impossible.

This end of Sun and life on Earth will take place just after 5 billion years (5 000 000 000). Sun is now in the middle of its life.

Although scientists have supposed that human species will be extinct in about 5 million years (5 000 000). So we won’t be here to see the Earth destroying.

How the Universe was born?

In Big Bang
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About 13.7 billion years ago all the materia of the universe was condensed in one spot, called singularity, which size was blinding small and density infinite. When singularity was condensed to as small it can be, it exploded. It's called the Big Bang, because it was the biggest explosion of the universe. There was no sound in it, because there were no air in which the sonic waves would travel, so the big "bang" is relatively misleading term. In just a fraction of second the whole universe spread out of that spot. It wasn't like we know it now, just large amount of chemical elements. Elements mixed together creating new elements and forming objects. Elements were first in gas phase, but while cooling, some of them changed to liquid and solid form. Objects was first like fogs, then they condensed to solid objects. Gravity shaped the objects to spherical shape, like planets, planetoids (small planet-like objects), moons etc. If the object was heavy enough in physical mass, a nuclear reaction started in its core. The object started to radiate and it has become a star.
Stars born in nebulas (fogs full of materials for stars), when the star is condensed, there usually is lots of remain material (gas) around it. Gravity shapes the gas in the form of a disc that orbits around the star. The materia in the disc accumulates and form planets. If the spherical objects were near some object with greater mass, it probably started to orbit that object, so it became a moon. At first planets were gas, then liquid, then they cooled to solid objects. Planets heavy enough stayed in gas form. Planets have several layers inside them. For example Earths inner core is solid, outer core liquid, mantle viscous solid, outer mantle solid and crust solid. Most of the planets have just one core. Stars have layers also, core, mantle and surface.
Stars accumulated in galaxies, large drift of stars, and planets formed solar systems around the stars. This creative process is always under way, new stars and planets are constantly forming while others are being destroyed. The natural cause of universe.

No one can know what has happened before the Big Bang, because the time itself began then. Humans can make sharper and sharper telescopes and look further and further back in time, but we can't look back at the time, when time hasn't begun.