Is the remnant of the Solar System's "parent" star still drifting in outer space? As all elements which are heavier than iron, are only created through the process of either a supernova or a kilonova explosion. With us having naturally occurring elements such as uranium on Earth it shows that we (as both humans and the planet) were created after the said explosion occurred. Based on this I have a question: "Does the remnant of the said explosion still exist after more than 4 billion years or would it have radiated away?"
P.S.
My knowledge of physics is only at high-school level, if I am talking complete nonsense please let me know.
 A: The abundance mixture found in the Sun and ancient meteorites does not match the abundance mixture expected from the evolution and ultimate destruction of any star. That is unsurprising, because the solar system material was contributed to by the millions (or even a billion) stars that lived and died in our Galaxy before the Sun was born. e.g. How many times has the matter in our solar system been recycled from previous stars? and https://astronomy.stackexchange.com/questions/16311
There is therefore no chance of identifying the remnant of a progenitor, because there wasn't one.
Some more general comments:
Your statement about uranium is quite correct - most if not all of that will have been created in violent explosions, like supernovae and neutron star collisions. The remnants are black holes and neutron stars. They are still out there somewhere, though may have been ejected from the Galaxy.
Other heavy elements like barium, strontium and a host of others, were likely created by the s-process, and expelled in the winds of stars that never exploded and which ended up as white dwarfs. Such white dwarfs just continue to cool down. The coldest in the Galaxy have reached 3000K and can still be found. Nothing else will happen to them (if protons are stable, or unless they accrete more mass).
Much of the nickel and iron were created from the explosions of white dwarfs that became too massive by accreting material from companions. These "Type Ia supernova" explosions destroy the white dwarf, leaving no remnant at all.
All this stellar detritus is injected into the interstellar medium and then mixed up by relative motions within the Galaxy, tidal forces and turbulence that is stirred up by the explosions mentioned above.
A: There is no single "progenitor" star to the Sun. The Sun (and the solar system) where formed from gas enriched by heavy elements from many (possibly billions) supernovae and kilonovae of earlier stars in our galaxy. The black hole remnants of these events should be floating around in our galaxy. Some may have been flung out of the galaxy by the explosion that created them, while other may have merged to form bigger black holes, but the majority should still be around.
Although black hole should eventually evaporate due to Hawking radiation, this is a very slow process. In fact, the Hawking temperature of a stellar mass black hole is so low that any stellar remnants in our galaxy would be gaining more mass from absorbing the cosmic microwave background then they would lose from emitting Hawking radiation. We would need to first wait a long time for the universe to cooldown by many orders of magnitude before these black holes even start (the very slow) evaporation. 
