Are all organisms relatives of each other?

Yes - although 'family' has a specific technical meaning in evolution

 

Well the way you've posed the question it would necessarily imply that they are all 'cousins' or 'relatives' at a distance. This is because you make the assumption that all organisms came from a single original lifeform.

I do not see why this assumption is necessary though... it's perfectly plausible that all lifeforms that have existed on Earth may have different branches if we go far enough back... making them completely unrelated to other organisms.

Why?

Well I think it's unlikely that in the beginning stages of life there was only one cell that had formed with characteristics which allowed it to spread/become dominant. Plus they possibly could have merged with other cells forming yet newer cells. I find it far fetched that the origins of life trace all the way back to a single organism for all lifeforms that have existed.

 

All three branches of life archaea, bacteria, and eukaryote have DNA.
For your hypothesis to be true, life would have had to evolve in all three independantly in exactly the same way to create DNA with the same structure 3 times.

It is possible that life did start several times and even that completely unrelated forms existed at the same time (and haven't left any fossil record) but the DNA cell won out and all life today descended from it

 

Life started most likely with RNA and yeah since the molecules are floating around (amino acids) they will get gobbled up by cells and inside the cell all the magic happens.

 

Assuming multiple origins of DNA or RNA based life upon the Earth originating locally or cosmologically, it is more than likely that hybrid compositions would be existant. Nearly all organisms are viral and bacterial with a distant minority of more complex experiments, so the subject in question is for the most part about these.

 

course we are, we all came from stardust from a supernovae, which in turn came from the universe which is our mother