(i) is incorrect.

If force is applied normal to surface at point $X$

$\tau =F_y R\sin \theta$

Thus $\tau$ depends on $\theta$ and it is not constant

(ii) is incorrect

If force applied tangentially at S

$\tau =F\times R \ne 0$

But it will climb as mentioned in question.

If force is applied normal to surface at P then line of action of force will pass from Q and thus $\tau =0$

(iv) is incorrect.

If force is applied at P tangentially the $\tau =F\times 2R=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$