Should he marry a Christian Israeli Arab woman?

Firstly: 

It should be noted first of all that you did wrong by getting
to know this non-mahram woman. Islam has set out important guidelines
concerning the relationship between men and non-mahram women, so as to
protect Muslim men and women from falling into that which Allaah has
forbidden to us. That is so as to protect societies from the spread of
immorality and evil. This does not apply only to relationships between a
Muslim man with a non-mahram Muslim woman, but it also includes the
prohibition on doing that with kaafir women, but the shaytaan may tempt him
to commit this sin in the name of calling people to Allaah. 

We have previously discussed the ruling on corresponding and
talking with non-mahrams. See the answer to questions no.
22101,
26890,
23349 and
10221. 

Secondly: 

With regard to the ruling on marrying kaafir woman, it is
haraam, unless she is from the people of the Book – Jewish or Christian. A
Muslim may think that every woman who lives in America or Europe is a
Christian, or that if she lives with the Jews then she is Jewish, but this
is wrong. Just as there are those who are Muslim in name but are in fact
secular or communist, that also happens with them too, and on a greater
scale – there are many who are of the religion of their country in name,
without that having any reflection in reality. Hence the one who wants to
marry a non-Muslim woman must ascertain that the conditions for that are met
in the woman. They are: 

1.She should be of the people of
the Book – Jewish or Christian – even if she adheres to her deviant
religion, because these are the ones whose woman Allaah has permitted us to
marry. Allaah says (interpretation of the meaning):

“The food (slaughtered
cattle, eatable animals) of the people of the Scripture (Jews and
Christians) is lawful to you and yours is lawful to them. (Lawful to you in
marriage) are chaste women from the believers and chaste women from those
who were given the Scripture (Jews and Christians) before your time when you
have given their due Mahr (bridal-money given by the husband to his wife at
the time of marriage), desiring chastity (i.e. taking them in legal wedlock)
not committing illegal sexual intercourse, nor taking them as girlfriends”

[al-Maa’idah 5:5]

As for atheist, Buddhist and Magian (Zoroastrian) women, it
is not permissible to marry them. Allaah says (interpretation of the
meaning): 

“And do not marry Al-Mushrikaat (idolatresses) till they
believe (worship Allaah Alone). And indeed a slave woman who believes is
better than a (free) Mushrikah (idolatress), even though she pleases you”

[al-Baqarah 2:221]

2.She should be chaste, not
engaging in zina (fornication) or having boyfriends, because Allaah says in
the verse from al-Maa’idah quoted above: “chaste
women.”

3.The Muslim should be in charge.
So it should not be stipulated that they get married in the church, or that
the children should follow her religion, or anything else in which she and
her religion are given precedence at the expense of his religion. Allaah
says (interpretation of the meaning):

“And never will Allaah grant to the disbelievers a way (to
triumph) over the believers”

[al-Nisa’ 4:141]. 

This condition is not met in the case of one who marries a
woman from a western country, because he is governed by their laws and their
governments will take charge of all the children, and the governments and
embassies of those women will support them if he should decide to take his
children to a Muslim country against her wishes. 

Although it is permissible to marry women of the people of
the Book, Islam encourages us to marry Muslim women who are religiously
committed, because a Muslim’s life with his wife is all-encompassing and
includes chastity, lowering of the gaze, and protection and care of the
household and children. These and similar matters can only be achieved with
a religiously-committed Muslim woman.  

See the answer to question no.
12283, which is very important,
and also the answer to questions no.
20227 and 45645, which offer
more information on the negative effects of marrying non-Muslim women. 

Thirdly: 

What we advise you to do is to put this woman in touch with
Muslim women among your relatives or others who are involved in calling
people to Allaah, so they can encourage her to become Muslim and convince
her to enter the faith willingly, because there is the fear that her wanting
to become Muslim may be motivated by her love for you, so she would be
Muslim on the outside without any real faith in her heart. If she remained a
kaafir, she would not be able to marry you without the consent and agreement
of her kaafir wali (guardian) and the guardianship would pass to the Muslim
authorities – according to some scholars – if her kaafir guardian objects to
her marrying a Muslim because of his being Muslim, or if there is no one in
her family who follows her religion to whom guardianship could be passed.
But if she is Muslim, then even if there is no Muslim among her family who
could be her guardian, the Muslim qaadi (judge) or the one who acts in his
stead would be her guardian, because a kaafir cannot be the guardian of a
Muslim woman. 

If she becomes Muslim, then we think that she can escape from
her environment by marrying you, and move to your country, but you must be
careful to avoid falling into sin before that by looking at her, being alone
with her, and shaking hands with her, until you know that she has become
Muslim out of sincere conviction and has become a good Muslim, then you can
marry her in accordance with the Qur’aan and Sunnah. 

The Muslim should be cautious about marrying a kitaabi
(Jewish or Christian) woman, or a woman who has become Muslim because of her
love for her Muslim husband, for there is no guarantee that her becoming
Muslim does not have to do with meeting her immediate needs, and is not the
result of true conviction regarding the religion that she has joined. This
may have an effect on his life and the life of his children. In both cases
there is a risk to him and his children, and you should be even more
cautious if she is Jewish or she was living among the Jews, because the Jews
are known for plotting against the Muslims and using women to further those
plots. 

See the answer to questions no.
20884 and
33656, which describe how a woman
may become Muslim. 

We advise you to pray istikhaarah, details of which you will
find in questions no. 2217 and
11981. 

We ask Allaah to help you to repent sincerely and to guide
her to Islam, and to join you together in goodness if she accepts Islam and
becomes a good Muslim. 

And Allaah knows best.