Is it valid for someone who believes that i‘tikaaf can only be done in the three mosques (Makkah, Madinah and Jerusalem), but wants to seek Laylat al-Qadr, and has wishes and thinks that staying in the mosque at night during the last ten nights of Ramadan is an opportunity to attain what he wants from the Most High, the Almighty, the Eternal, may He be glorified and exalted, to do that? Please note that he is a scoundrel, a rascal and a wrongdoer who has no purpose in life, but he hopes that if he manages to be in a noble place at a noble time, with a sincere prayer, he will be able to change his life completely.

Praise
be to Allah

Firstly: 

If a person is a wrongdoer who has no purpose in life, he
should strive first of all to repent sincerely to Allah , and change his
ways from wrongdoing and sin to justice and obedience to Allah. 

Secondly: 

In fatwas no. 81134 and
49006, we explained that it is valid to observe
i‘tikaaf in all mosques, and it is not limited only to the three mosques. 

Thirdly: 

With regard to the answer to what you asked about, if he
follows a scholar who says that i‘tikaaf is only valid in the three mosques,
there is nothing wrong with him staying in the mosque during the last ten
nights of Ramadan. This applies even if it is not i‘tikaaf, according to his
belief; staying in the mosque for the purpose of prayer, dhikr, reading
Qur’an and waiting for the prayer is a virtuous deed in and of itself. The
Prophet (blessings and peace of Allah be upon him) said: “If he prays (i.e.,
in the mosque), the angels will continue to send blessings upon him so long
as he remains in the place where he prayed, (saying): ‘O Allah send
blessings upon him, O Allah have mercy upon him.’ And one of you remains in
a state of prayer so long as he is waiting for the prayer.”

Narrated by al-Bukhaari (648) and Muslim (649). 

Al-Bayhaqi narrated in Shu‘ab al-Eemaan (2943) that
‘Amr ibn Maymoon al-Awdi said: The companions of the Messenger of Allah
(blessings and peace of Allah be upon him) told us that the mosques are the
houses of Allah on earth, and it is incumbent upon Allah to honour those who
visit Him in them. Classed as saheeh by al-Albaani in Silsilat al-Ahaadeeth
as-Saheehah (1169). 

In addition to that, it also has the benefit of allowing one
to focus on worshipping Allah, may He be exalted, and to leave behind
worldly matters that may distract one. 

And Allah knows best.