Given below are two statements: Statement-I: An elevator can go up...

When elevator is moving with uniform speed $T = {F}_{g}$, as the net force along the vertical direction should be zero.

Therefore, Statement-I is true.

Now, when elevator is going down with increasing speed, its acceleration is downward.
Hence,

$W - N = ma ⇒ W - N = \dfrac{W}{g} \times a$

$⇒ N = W\left(1 - \dfrac{a}{g}\right)$

Clearly, normal reaction is less than weight. So Statement-II is false.