statistics

1. You may say so, but the essence of hypothesis testing is not on absolute value of the p-value but on how stringent you have set the confidence level on accepting a Type II error. Usually the confidence level is set at p<=0.05. Once the p-value is <=0.05 after computation, you may reject the null hypothesis with 95% of confidence level that the null hypothesis is not rejected wrongly.

2. The result is simple.
(a) There is no relationship between two variables if and only if r=0
(c) There is no implication on which variable has greater value than the other from the r
(d) The (-) sign does not indicate anything about the characteristics of a particular variable. It only indicates the correlation between the two variables.
(b) This is the only true results among these 4. (-) indicates that the two variables are negatively correlated to each other.

And so, the smaller is the p-value, the stronger is the evidence against the null hypothesis, is it true or false ? Can I say that the statement is true ?

r = -0.3, it means there is some weak negative correlation between x & y. The conclusion is that the slope is negative.
If we exchange data x with data y, the correlation factor will remain the same, no relation to whether x is larger or not. Also variance must be >= 0, it is the sum of squares.