You might know that a direct consequence of Newton's second law ($F=ma$) is that the total change in kinetic energy of a body $\Delta K$ is equal to the total work $W$ of external forces, i.e.
$$\Delta K = W$$
If the difference in kinetic energy is zero ($\Delta K = 0$) then that implies
$$\Delta K = W = 0$$
so you get that the total work $W$ is 0. Clearly that implies (3) is false as it would mean the potential energy is 0.
We can split the work into the work coming from conservative forces $W_c$ and the work done by the rest of the forces $W_R$ so that
$$\Delta K = W_c+W_R$$
Which means also that if $W=0$ the work of conservative force is equal and opposite to that of non-conservative forces ($W_c=-W_R$), and that's all we learn in this case.
From the above equation, we also get, shuffling the terms
$$-W_c= W_R-\Delta K$$
which clearly indicates that the negative work of the conservative forces is not the potential energy, so (2) is false.
The righ answer is (1), by exclusion.
Potential energy is indeed defined as the positive work done by conservative forces which in our case is $W_c$, so if we set $W_c=U$ then
$$U=\Delta K - W_R$$ i.e. you could define potential energy also as the change in energy of your system minus the work done by non - conservative forces.
That is actually not the definition of potential energy but rather a consequence of it. The actual definition is $$U=W_c$$ or more in general, given a conservative force $F$ then if we go from a point in space $A$ to a point $B$ along a path $\gamma$ then the potential energy is the work down along that path by $F$.
The reason you need a conservative field to define a potential energy is that the above definition does not depend on the path your system takes from a point $A$ to a point $B$ so that whatever path you take $U$ is always the same. That is not true for $W_R$ or $\Delta K$ in general, it's only true for their difference (i.e. $W_c$).
From the above relationship and using $W_c=U$ i.e. $$\Delta K = W = U+W_R$$ we learn alternative definitions of $U$
1 - as the positive work done by conservative forces [not negative as in (2)]
2 - as the negative work done by non-conservative forces when $\Delta K =0 $ because then $U=-W_R$ [not of the total work, as in (3)]
3 - as $U = \Delta K -W_R$
Hope this clear things up.