Do these answers work even when we change the values? So I know that these are both true, but if I change the values would they still be true? Do these statements hold for any value?

A) Suppose f is a flow of value 50 from s to t in a flow network G. The capacity of the minimum s-t cut in G is equal to 50. 

Suppose we were using 100 or maybe 75 instead of 50. Is this still true?

B) Suppose f is a flow of value 100 from s to t in a flow network G and there is an s-t cut of capacity 100. Then there are no s --> t paths in the residual graph Gf. 

If we use 80, 60, 20 and so on is this still true? What about for odd numbers?
The value of any $st$-flow is at most the value of any $st$-cut, and they are equal if and only if the flow value is maximized and the cut value is minimized. Thus, statement (A) is false since $f$ isn't necessarily a maximum flow (since you claim (A) is true, maybe you forgot to mention that $f$ is a maximum flow, or you meant to say that the value of the cut is at least 50?).
Statement (B) is true, since if there is a flow and cut of equal value, then the flow is a maximum flow and the residual graph has no path from $s$ to $t$.

Of course, the actual values don't matter. Only the relationship between the flow value and cut value is relevant.