If a person looks at the Mus-haf without moving his lips, will he be rewarded for that?

There is nothing to prevent a person looking at the Qur’aan
without reciting it, in order to ponder its meanings and understand
it. But he is not considered to be “reading” Qur’aan when he does that,
and he does not earn the reward for reading it unless he pronounces
(the words of) the Qur’aan, even if those around him do not hear him.
The Prophet (peace and blessings
of Allaah be upon him) said:

“Read the Qur’aan, for it will come on the Day of Resurrection to
intercede for its companions.” (Narrated by Muslim).

What he (peace and blessings
of Allaah be upon him) meant by its companions is those who act upon
it, as stated in other ahaadeeth. The Prophet
(peace and blessings of Allaah be upon him) said: “Whoever reads one
letter of the Qur’aan will have one hasanah, and the hasanah will be
rewarded tenfold.”  (Narrated by al-Tirmidhi and al-Daarimi with
a saheeh isnaad). And one cannot be counted as reading Qur’aan unless
once actually pronounces it.

And Allaah is the source of strength.