I have two questions:

From the definition of the Jones polynomial as the normalization of the Kauffman bracket $(-A^3)^{-w(D)} \langle D\rangle$ and substituting $A\rightarrow t^{-1/4}$, how does one obtain the skein relation for the Jones polynomial, $(t^{1/2}-t^{-1/2}) V_0(K)=t^{-1}V(K_+)-tV(K_-)$?

If we take the definition of the HOMFLPT polynomial $lP(L_+)+l^{-1}P(L_-)+mP(L_0)=0$, how do I show that the Jones polynomial is a special case of the HOMFLYPT in the sence that $V(K_1) = V(K_2) \Rightarrow P(K_1)=P(K_2).$ If we take $m=-(t^{1/2}-t^{-1/2})$ and $l=t^{-1}$, the signs don't match (I know that we can take another definition where it works, but I'm wondering from this one).

Can the above two questions be answered using an elementary or combinatorial approach?

In addition, is there a reference for counterexamples that show that the HOMFLYPT is stronger than the Alexander, Jones, Kauffman?