Where is the "paradox"? I assume that you mean that by pure hypothesis testing both Alice and Bob reject the null hypothesis at the alpha=0.05 level, for example. The fact that the p-value is irrelevant is by design: you perform the test and either you reject the null hypothesis or you don't. But in fact most people won't do "pure" hypothesis testing and will conclude (somewhat incorrectly) that the evidence against the null hypothesis is indeed stronger in Bob's experiment.

Edit: and why would be the answer to the second question "no"? The hypothesis testing procedure doesn't provide any point estimate at all so the question doesn't really mean anything in that setting.