Finding if two points on elliptic curve are related
No you can't.

I'll make the argument over the integers, it directly transfers to ECC points.

Suppose you have two integers $c,e\in\mathbb Z$. You can now prove for every $a\in\mathbb Z$ that $c$ and $e$ have $a$ "in common".

For this you simply pick $b=c-a$ and $d=e-a$ and now you have the "proof" that both have $a$ in common. Note how no restrictions whatsoever have been placed on $a,c,e$ so it works with all triples.