1. Recall the energy relations for a satellite in a bound circular orbit

For a satellite of mass $m$ orbiting Earth of mass $M$ at radius $r$:

• Gravitational potential energy: $U=-\frac{GMm}{r}$
• Orbital speed from gravitational force providing centripetal force: $\frac{mv^2}{r}=\frac{GMm}{r^2}\implies v^2=\frac{GM}{r}$
• Hence kinetic energy: $K=\frac{1}{2}mv^2=\frac{1}{2}m\cdot \frac{GM}{r}=\frac{GMm}{2r}$

2. Find total energy

$E=K+U=\frac{GMm}{2r}-\frac{GMm}{r}=-\frac{GMm}{2r}$

So for a satellite in orbit: $K=-E$ and $U=2E$

since $2E=2\left(-\frac{GMm}{2r}\right)=-\frac{GMm}{r}=U$

3. Check Statement I

Statement I says: potential energy is $\frac{E}{2}$.

But actually, $U=2E$ not $U=\frac{E}{2}$

So Statement I is incorrect.

4. Check Statement II

Statement II says: kinetic energy is equal to half the magnitude of total energy $E$.

Now, $|E|=\frac{GMm}{2r}$ And $K=\frac{GMm}{2r}=|E|$

Thus kinetic energy is equal to the full magnitude of total energy, not half of it.

So Statement II is also incorrect.

5. Choose the correct option

Therefore, both Statement I and Statement II are incorrect.

So the correct option is: $\boxed{A}$

6. Comparison with stored answer

Stored correct answer: $A$

My derived answer also is $A$, so they agree.