2) p-value < alpha DOES induces that H0 is not true.
The Critical Value, C, by definition, is such that prob(W>C)= alpha, i.e., the more extreme value W must show if the Null Hypothesis is true, for a right tail significance test. We are testing the parameter p: Suppose that you fail to reject H0: p=2 at alpha=5% significance level. This means that W the test statistics value say, w0, is such that the probability to get from random data, same sample sizes, prob(W>w0) > alpha when p=2. In consequence the condition p-value < alpha induces the idea that H0 must be rejected. Compare with: If H0 is true the associated test statistics W must not be grater than Critical Value, C, corresponding to alpha = 5%. or the sample is not random: _____From the test I got w0<C, therefore or H0 is possibly untrue or data is not random. But, be careful, is merely an inductive reasoning: it is miles apart to be a deductive then exact result as:___all human are mortals,___Socrates is human,___(therefore) Socrates is mortal. The first two premises being stated compel the conclusion without any doubt.
Note that some researchers do not agree that the condition p-value<alpha is indicative that H0 should be rejected. They argue that are two entirely different entities then unable to be compared: alpha is an arbitrary set-before-test value, on contrary p is a random variable happening as a result of the test. Of course irrefutable in what concern the genesis but I do not see (and mostly people) how they are unable to be used at inductive terms.
Once p-value < alpha we are not allowed to state that H0 is true, no way. Ronald Fisher said it clearly at the time he rediscovered significance test: Any Hypothesis is liable to be proved true.