Looks like there is counterexample to Proposition related to abc conjecture. Confusion is likely.

From RATIONAL AND INTEGRAL POINTS ON QUADRATIC TWISTS OF A GIVEN HYPERELLIPTIC CURVE, Andrew Granville

p. 11, Proposition 2 b

Suppose that $G(x,y) \in \mathbb{C}[x,y]$ is homogeneous without any repeated factors. For any coprime polynomials $r(t),s(t) \in \mathbb{C}[t]$, we have

$$ \#\{\alpha \in \mathbb{C}: G(r(\alpha),s(\alpha))=0\} \ge \max\{\deg(r),\deg(s)\}(\deg(G)-2) + 2. $$

$\#\{\alpha \in \mathbb{C}: G(r(\alpha),s(\alpha))=0\}$ counts the distinct zeros and equals the degree of the radical of $G(r(t),s(t))$.

Explicit counterexample.

Let $G(x,y)=x^4+xy^3,r(t)=8t^3 + 64,s(t)=t^4 - 64t$

We have:

$$ G(r(t),s(t))=\left(8\right) \cdot (t + 2) \cdot (t^{2} - 2 t + 4) \cdot (t^{2} + 4 t - 8)^{2} \cdot (t^{4} - 4 t^{3} + 24 t^{2} + 32 t + 64)^{2} $$

So $G(r(t),s(t))$ have $9$ distinct zeros.

By the Proposition $9 \ge (( (4\cdot(4-2)+2)=10)$ which is false.

Q1 Is this really counterexample?

The Proposition is unconditional and this doesn't appear to contradict abc.

The errata of the paper doesn't address this.

Andrew Granville ask for other $G$. There are constructions.

Here is example in computer readable form with t=x:

G=x^3*y + x*y^3 + 8*y^4
r=x^16 - 40*x^14 - 4352*x^13 + 348*x^12 + 1024*x^11 + 189416*x^10 + 14080*x^9 + 622022*x^8 + 4485120*x^7 + 910312*x^6 + 13647104*x^5 + 65163612*x^4 + 3943424*x^3 + 46235608*x^2 + 134216960*x - 1050623
s=16*x^15 + 176*x^13 + 5248*x^12 + 400*x^11 + 30976*x^10 + 433584*x^9 - 4224*x^8 + 343472*x^7 + 486912*x^6 - 392816*x^5 - 4060288*x^4 - 16662352*x^3 + 1313024*x^2 + 8413200*x + 33685632