1) It is false. There is a simple counter example. If P(B)=1 and P(A)=0.5 then P(A or B)=1 and P(A)P(B)=0.5. The question did not state that A and B cannot occur at the same time so their probabilities can sum to be greater than 1.

I think you might have misstyped P(A)+P(B) as P(A)P(B), if that is the case then it is also false, only if A and B are mutually exclusive P(A)+P(B) = P(A or B)

2) Confidence intervals cannot be used if what you are dealing with is not quantitative.